In this HackerRank Counting Road Networks problem solution, You must answer Q queries, where each query consists of some N denoting the number of cities Lukas wants to design a bidirectional network of roads for. For each query, find and print the number of ways he can build roads connecting n cities on a new line; as the number of ways can be quite large, print it modulo 663224321.

hackerrank counting road networks problem solution


Problem solution in Java.

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class E2 {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
    
    void solve()
    {
        int n = 100005;
        long[] a = new long[n];
        int mod = 663224321;
        for(int i = 0;i < n;i++){
            a[i] = pow(2, (long)i*(i-1)/2, mod);
        }
        int[][] fif = enumFIF(100005, mod);
        long[] ta = transformLogarithmically(a, fif);
        for(int Q = ni();Q > 0;Q--){
            out.println(ta[ni()]);
        }
    }
    
    public static int[][] enumFIF(int n, int mod) {
        int[] f = new int[n + 1];
        int[] invf = new int[n + 1];
        f[0] = 1;
        for (int i = 1; i <= n; i++) {
            f[i] = (int) ((long) f[i - 1] * i % mod);
        }
        long a = f[n];
        long b = mod;
        long p = 1, q = 0;
        while (b > 0) {
            long c = a / b;
            long d;
            d = a;
            a = b;
            b = d % b;
            d = p;
            p = q;
            q = d - c * q;
        }
        invf[n] = (int) (p < 0 ? p + mod : p);
        for (int i = n - 1; i >= 0; i--) {
            invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod);
        }
        return new int[][] { f, invf };
    }

    
    public static long pow(long a, long n, long mod) {
       
        long ret = 1;
        int x = 63 - Long.numberOfLeadingZeros(n);
        for (; x >= 0; x--) {
            ret = ret * ret % mod;
            if (n << 63 - x < 0)
                ret = ret * a % mod;
        }
        return ret;
    }
    
    public static int mod = 663224321;
    public static int G = 3;
    
    public static long[] mul(long[] a, long[] b)
    {
        return Arrays.copyOf(convoluteSimply(a, b, mod, G), a.length+b.length-1);
    }
    
    public static long[] mul(long[] a, long[] b, int lim)
    {
        return Arrays.copyOf(convoluteSimply(a, b, mod, G), lim);
    }
    
    public static long[] mulnaive(long[] a, long[] b)
    {
        long[] c = new long[a.length+b.length-1];
        long big = 8L*mod*mod;
        for(int i = 0;i < a.length;i++){
            for(int j = 0;j < b.length;j++){
                c[i+j] += a[i]*b[j];
                if(c[i+j] >= big)c[i+j] -= big;
            }
        }
        for(int i = 0;i < c.length;i++)c[i] %= mod;
        return c;
    }
    
    public static long[] mulnaive(long[] a, long[] b, int lim)
    {
        long[] c = new long[lim];
        long big = 8L*mod*mod;
        for(int i = 0;i < a.length;i++){
            for(int j = 0;j < b.length && i+j < lim;j++){
                c[i+j] += a[i]*b[j];
                if(c[i+j] >= big)c[i+j] -= big;
            }
        }
        for(int i = 0;i < c.length;i++)c[i] %= mod;
        return c;
    }
    
    public static long[] add(long[] a, long[] b)
    {
        long[] c = new long[Math.max(a.length, b.length)];
        for(int i = 0;i < a.length;i++)c[i] += a[i];
        for(int i = 0;i < b.length;i++)c[i] += b[i];
        for(int i = 0;i < c.length;i++)if(c[i] >= mod)c[i] -= mod;
        return c;
    }
    
    public static long[] add(long[] a, long[] b, int lim)
    {
        long[] c = new long[lim];
        for(int i = 0;i < a.length && i < lim;i++)c[i] += a[i];
        for(int i = 0;i < b.length && i < lim;i++)c[i] += b[i];
        for(int i = 0;i < c.length;i++)if(c[i] >= mod)c[i] -= mod;
        return c;
    }
    
    public static long[] sub(long[] a, long[] b)
    {
        long[] c = new long[Math.max(a.length, b.length)];
        for(int i = 0;i < a.length;i++)c[i] += a[i];
        for(int i = 0;i < b.length;i++)c[i] -= b[i];
        for(int i = 0;i < c.length;i++)if(c[i] < 0)c[i] += mod;
        return c;
    }
    
    public static long[] sub(long[] a, long[] b, int lim)
    {
        long[] c = new long[lim];
        for(int i = 0;i < a.length && i < lim;i++)c[i] += a[i];
        for(int i = 0;i < b.length && i < lim;i++)c[i] -= b[i];
        for(int i = 0;i < c.length;i++)if(c[i] < 0)c[i] += mod;
        return c;
    }
    
    
    public static long[] inv(long[] p)
    {
        int n = p.length;
        long[] f = {invl(p[0], mod)};
        for(int i = 0;i < p.length;i++){
            if(p[i] == 0)continue;
            p[i] = mod-p[i];
        }
        for(int i = 1;i < 2*n;i*=2){
            long[] f2 = mul(f, f, Math.min(n, 2*i));
            long[] f2p = mul(f2, Arrays.copyOf(p, i), Math.min(n, 2*i));
            for(int j = 0;j < f.length;j++){
                f2p[j] += 2L*f[j];
                if(f2p[j] >= mod)f2p[j] -= mod;
                if(f2p[j] >= mod)f2p[j] -= mod;
            }
            f = f2p;
        }
        for(int i = 0;i < p.length;i++){
            if(p[i] == 0)continue;
            p[i] = mod-p[i];
        }
        return f;
    }
    
    
    public static long[] d(long[] p)
    {
        long[] q = new long[p.length];
        for(int i = 0;i < p.length-1;i++){
            q[i] = p[i+1] * (i+1) % mod;
        }
        return q;
    }
    
    
    public static long[] i(long[] p)
    {
        long[] q = new long[p.length];
        for(int i = 0;i < p.length-1;i++){
            q[i+1] = p[i] * invl(i+1, mod) % mod;
        }
        return q;
    }
    
    
    public static long[] exp(long[] p)
    {
        int n = p.length;
        long[] f = {p[0]};
        for(int i = 1;i < 2*n;i*=2){
            long[] ii = ln(f);
            long[] sub = sub(ii, p, Math.min(n, 2*i));
            if(--sub[0] < 0)sub[0] += mod;
            for(int j = 0;j < 2*i && j < n;j++){
                sub[j] = mod-sub[j];
                if(sub[j] == mod)sub[j] = 0;
            }
            f = mul(sub, f, Math.min(n, 2*i));

        }
        return f;
    }
    
   
    public static long[] ln(long[] f)
    {
        long[] ret = i(mul(d(f), inv(f)));
        ret[0] = f[0];
        return ret;
    }
    
   
    public static long[] pow(long[] p, int K)
    {
        int n = p.length;
        long[] lnp = ln(p);
        for(int i = 1;i < lnp.length;i++)lnp[i] = lnp[i] * K % mod;
        lnp[0] = pow(p[0], K, mod); // go well for some reason
        return exp(Arrays.copyOf(lnp, n));
    }
    
   
    public static long[] divf(long[] a, int[][] fif)
    {
        for(int i = 0;i < a.length;i++)a[i] = a[i] * fif[1][i] % mod;
        return a;
    }
    
    
    public static long[] mulf(long[] a, int[][] fif)
    {
        for(int i = 0;i < a.length;i++)a[i] = a[i] * fif[0][i] % mod;
        return a;
    }
    
    public static long[] transformExponentially(long[] a, int[][] fif)
    {
        return mulf(exp(divf(Arrays.copyOf(a, a.length), fif)), fif);
    }
    
    public static long[] transformLogarithmically(long[] a, int[][] fif)
    {
        return mulf(Arrays.copyOf(ln(divf(Arrays.copyOf(a, a.length), fif)), a.length), fif);
    }
    
    public static long invl(long a, long mod) {
        long b = mod;
        long p = 1, q = 0;
        while (b > 0) {
            long c = a / b;
            long d;
            d = a;
            a = b;
            b = d % b;
            d = p;
            p = q;
            q = d - c * q;
        }
        return p < 0 ? p + mod : p;
    }
    
    public static long[] reverse(long[] p)
    {
        long[] ret = new long[p.length];
        for(int i = 0;i < p.length;i++){
            ret[i] = p[p.length-1-i];
        }
        return ret;
    }
    
    public static long[] reverse(long[] p, int lim)
    {
        long[] ret = new long[lim];
        for(int i = 0;i < lim && i < p.length;i++){
            ret[i] = p[p.length-1-i];
        }
        return ret;
    }
    
   
    public static long[][] div(long[] p, long[] q)
    {
        if(p.length < q.length)return new long[][]{new long[0], Arrays.copyOf(p, p.length)};
        long[] rp = reverse(p, p.length-q.length+1);
        long[] rq = reverse(q, p.length-q.length+1);
        long[] rd = mul(rp, inv(rq), p.length-q.length+1);
        long[] d = reverse(rd, p.length-q.length+1);
        long[] r = sub(p, mul(d, q, q.length-1), q.length-1);
        return new long[][]{d, r};
    }

    public static long[] substitute(long[] p, long[] xs)
    {
        return descendProductTree(p, buildProductTree(xs));
    }
    
    public static long[][] buildProductTree(long[] xs)
    {
        int m = Integer.highestOneBit(xs.length)*4;
        long[][] ms = new long[m][];
        for(int i = 0;i < xs.length;i++){
            ms[m/2+i] = new long[]{mod-xs[i], 1};
        }
        for(int i = m/2-1;i >= 1;i--){
            if(ms[2*i] == null){
                ms[i] = null;
            }else if(ms[2*i+1] == null){
                ms[i] = ms[2*i];
            }else{
                ms[i] = mul(ms[2*i], ms[2*i+1]);
            }
        }
        return ms;
    }
    
    public static long[] descendProductTree(long[] p, long[][] pt)
    {
        long[] rets = new long[pt[1].length-1];
        dfs(p, pt, 1, rets);
        return rets;
    }
    
    private static void dfs(long[] p, long[][] pt, int cur, long[] rets)
    {
        if(pt[cur] == null)return;
        if(cur >= pt.length/2){
            rets[cur-pt.length/2] = p[0];
        }else{
           
            
            if(p.length >= 1500){
                if(pt[2*cur+1] != null){
                    long[][] qr0 = div(p, pt[2*cur]);
                    dfs(qr0[1], pt, cur*2, rets);
                    long[][] qr1 = div(p, pt[2*cur+1]);
                    dfs(qr1[1], pt, cur*2+1, rets);
                }else if(pt[2*cur] != null){
                    long[] nex = cur == 1 ? div(p, pt[2*cur])[1] : p;
                    dfs(nex, pt, cur*2, rets);
                }
            }else{
                if(pt[2*cur+1] != null){
                    dfs(modnaive(p, pt[2*cur]), pt, cur*2, rets);
                    dfs(modnaive(p, pt[2*cur+1]), pt, cur*2+1, rets);
                }else if(pt[2*cur] != null){
                    long[] nex = cur == 1 ? modnaive(p, pt[2*cur]) : p;
                    dfs(nex, pt, cur*2, rets);
                }
            }
        }
    }
    
    
    public static long[][] divnaive(long[] a, long[] b)
    {
        int n = a.length, m = b.length;
        if(n-m+1 <= 0)return new long[][]{new long[0], Arrays.copyOf(a, n)};
        long[] r = Arrays.copyOf(a, n);
        long[] q = new long[n-m+1];
        long ib = invl(b[m-1], mod);
        for(int i = n-1;i >= m-1;i--){
            long x = ib * r[i] % mod;
            q[i-(m-1)] = x;
            for(int j = m-1;j >= 0;j--){
                r[i+j-(m-1)] -= b[j]*x;
                r[i+j-(m-1)] %= mod;
                if(r[i+j-(m-1)] < 0)r[i+j-(m-1)] += mod;

            }
        }
        return new long[][]{q, Arrays.copyOf(r, m-1)};
    }
    
    public static long[] modnaive(long[] a, long[] b)
    {
        int n = a.length, m = b.length;
        if(n-m+1 <= 0)return a;
        long[] r = Arrays.copyOf(a, n);
        long ib = invl(b[m-1], mod);
        for(int i = n-1;i >= m-1;i--){
            long x = ib * r[i] % mod;
            for(int j = m-1;j >= 0;j--){
                r[i+j-(m-1)] -= b[j]*x;
                r[i+j-(m-1)] %= mod;
                if(r[i+j-(m-1)] < 0)r[i+j-(m-1)] += mod;

            }
        }
        return Arrays.copyOf(r, m-1);
    }

    public static final int[] NTTPrimes = {1053818881, 1051721729, 1045430273, 1012924417, 1007681537, 1004535809, 998244353, 985661441, 976224257, 975175681};
    public static final int[] NTTPrimitiveRoots = {7, 6, 3, 5, 3, 3, 3, 3, 3, 17};

    
    public static long[] convoluteSimply(long[] a, long[] b, int P, int g)
    {
        int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);
        long[] fa = nttmb(a, m, false, P, g);
        long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
        for(int i = 0;i < m;i++){
            fa[i] = fa[i]*fb[i]%P;
        }
        return nttmb(fa, m, true, P, g);
    }
    
    public static long[] convolute(long[] a, long[] b)
    {
        int USE = 2;
        int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);
        long[][] fs = new long[USE][];
        for(int k = 0;k < USE;k++){
            int P = NTTPrimes[k], g = NTTPrimitiveRoots[k];
            long[] fa = nttmb(a, m, false, P, g);
            long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
            for(int i = 0;i < m;i++){
                fa[i] = fa[i]*fb[i]%P;
            }
            fs[k] = nttmb(fa, m, true, P, g);
        }
        
        int[] mods = Arrays.copyOf(NTTPrimes, USE);
        long[] gammas = garnerPrepare(mods);
        int[] buf = new int[USE];
        for(int i = 0;i < fs[0].length;i++){
            for(int j = 0;j < USE;j++)buf[j] = (int)fs[j][i];
            long[] res = garnerBatch(buf, mods, gammas);
            long ret = 0;
            for(int j = res.length-1;j >= 0;j--)ret = ret * mods[j] + res[j];
            fs[0][i] = ret;
        }
        return fs[0];
    }
    
    public static long[] convolute(long[] a, long[] b, int USE, int mod)
    {
        int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length)-1)<<2);
        long[][] fs = new long[USE][];
        for(int k = 0;k < USE;k++){
            int P = NTTPrimes[k], g = NTTPrimitiveRoots[k];
            long[] fa = nttmb(a, m, false, P, g);
            long[] fb = a == b ? fa : nttmb(b, m, false, P, g);
            for(int i = 0;i < m;i++){
                fa[i] = fa[i]*fb[i]%P;
            }
            fs[k] = nttmb(fa, m, true, P, g);
        }
        
        int[] mods = Arrays.copyOf(NTTPrimes, USE);
        long[] gammas = garnerPrepare(mods);
        int[] buf = new int[USE];
        for(int i = 0;i < fs[0].length;i++){
            for(int j = 0;j < USE;j++)buf[j] = (int)fs[j][i];
            long[] res = garnerBatch(buf, mods, gammas);
            long ret = 0;
            for(int j = res.length-1;j >= 0;j--)ret = (ret * mods[j] + res[j]) % mod;
            fs[0][i] = ret;
        }
        return fs[0];
    }
    
    
    private static long[] nttmb(long[] src, int n, boolean inverse, int P, int g)
    {
        long[] dst = Arrays.copyOf(src, n);
        
        int h = Integer.numberOfTrailingZeros(n);
        long K = Integer.highestOneBit(P)<<1;
        int H = Long.numberOfTrailingZeros(K)*2;
        long M = K*K/P;
        
        int[] wws = new int[1<<h-1];
        long dw = inverse ? pow(g, P-1-(P-1)/n, P) : pow(g, (P-1)/n, P);
        long w = (1L<<32)%P;
        for(int k = 0;k < 1<<h-1;k++){
            wws[k] = (int)w;
            w = modh(w*dw, M, H, P);
        }
        long J = invl(P, 1L<<32);
        for(int i = 0;i < h;i++){
            for(int j = 0;j < 1<<i;j++){
                for(int k = 0, s = j<<h-i, t = s|1<<h-i-1;k < 1<<h-i-1;k++,s++,t++){
                    long u = (dst[s] - dst[t] + 2*P)*wws[k];
                    dst[s] += dst[t];
                    if(dst[s] >= 2*P)dst[s] -= 2*P;
//                    long Q = (u&(1L<<32)-1)*J&(1L<<32)-1;
                    long Q = (u<<32)*J>>>32;
                    dst[t] = (u>>>32)-(Q*P>>>32)+P;
                }
            }
            if(i < h-1){
                for(int k = 0;k < 1<<h-i-2;k++)wws[k] = wws[k*2];
            }
        }
        for(int i = 0;i < n;i++){
            if(dst[i] >= P)dst[i] -= P;
        }
        for(int i = 0;i < n;i++){
            int rev = Integer.reverse(i)>>>-h;
            if(i < rev){
                long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d;
            }
        }
        
        if(inverse){
            long in = invl(n, P);
            for(int i = 0;i < n;i++)dst[i] = modh(dst[i]*in, M, H, P);
        }
        
        return dst;
    }
    
    static final long mask = (1L<<31)-1;
    
    public static long modh(long a, long M, int h, int mod)
    {
        long r = a-((M*(a&mask)>>>31)+M*(a>>>31)>>>h-31)*mod;
        return r < mod ? r : r-mod;
    }
    
    private static long[] garnerPrepare(int[] m)
    {
        int n = m.length;
        assert n == m.length;
        if(n == 0)return new long[0];
        long[] gamma = new long[n];
        for(int k = 1;k < n;k++){
            long prod = 1;
            for(int i = 0;i < k;i++){
                prod = prod * m[i] % m[k];
            }
            gamma[k] = invl(prod, m[k]);
        }
        return gamma;
    }
    
    private static long[] garnerBatch(int[] u, int[] m, long[] gamma)
    {
        int n = u.length;
        assert n == m.length;
        long[] v = new long[n];
        v[0] = u[0];
        for(int k = 1;k < n;k++){
            long temp = v[k-1];
            for(int j = k-2;j >= 0;j--){
                temp = (temp * m[j] + v[j]) % m[k];
            }
            v[k] = (u[k] - temp) * gamma[k] % m[k];
            if(v[k] < 0)v[k] += m[k];
        }
        return v;
    }
    
    void run() throws Exception
    {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
    }
    
    public static void main(String[] args) throws Exception { new E2().run(); }
    
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;
    
    private int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    
    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    
    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
}

{"mode":"full","isActive":false}


Problem solution in C++.

#include <bits/stdc++.h>
using namespace std;
const int MAXN = 300005;
const int root = 1489;
const int root_1 = 296201594;
const int root_pw = (1<<19);
const long long int MOD = 663224321;
long long int fact[MAXN], invfact[MAXN], pow2[MAXN], all_graphs[MAXN], poly1[MAXN], poly2[MAXN];
long long int power(long long int a, int b)
{
    if(!b)
        return 1;
    long long int ans = power(a,b/2);
    ans = (ans*ans)%MOD;
    if(b%2)
        ans = (ans*a)%MOD;
    return ans;
}

void fft (vector<long long int> &a, bool invert)
{
    int n = (int) a.size(); 
    for (int i = 1, j = 0; i < n; ++i)
    {
        int bit = n >> 1;
        for (; j >= bit; bit>>=1)
            j-=bit;
        j+=bit;
        if(i < j)
            swap(a[i], a[j]);
    }
    for (int len = 2; len <= n; len<<=1)
    {
        long long int wlen = invert ? root_1 : root;
        for (int i = len; i < root_pw; i<<=1)
            wlen = (wlen*wlen)%MOD;
        for (int i = 0; i < n; i+=len)
        {
            long long int w = 1;
            for (int j = 0; j < len/2; ++j)
            {
                int u = a[i+j],  v = (a[i+j+len/2]*w)%MOD;
                a[i+j] = u+v < MOD ? u+v : u+v-MOD;
                a[i+j+len/2] = u-v >= 0 ? u-v : u-v+MOD;
                w = (w*wlen)%MOD;
            }
        }
    }
    if(invert)
    {
        int nrev = power(n, MOD-2);
        for (int i=0; i<n; ++i)
            a[i] = (a[i]*nrev)%MOD;
    }
}
void multiply(vector <long long int> &a, vector <long long int> &b, vector <long long int> &c)
{
    vector <long long int> ta(a.begin(), a.end()), tb(b.begin(), b.end()), tc;
    int sz = 2*a.size();
    ta.resize(sz);
    tb.resize(sz);
    fft(ta,false);
    fft(tb,false);
    for (int i = 0; i < sz; ++i)
    {
        ta[i] = (1ll*ta[i]*tb[i])%MOD;
    }
    fft(ta,true);
    c = ta;
}
void dnc(int l, int r)
{
    if(l+1 == r)
    {
        poly2[l] = (all_graphs[l]*invfact[l-1] + MOD - poly2[l])%MOD;
    }
    else
    {
        int m = (l + r)/2;
        dnc(l,m);
        dnc(m,r);
    }
    vector <long long int> p1, p2, ans;
    int sz = r - l;
    for (int i = sz; i < 2*sz; ++i)
    {
        p1.push_back(poly1[i]);
    }
    for (int i = l; i < r; ++i)
    {
        p2.push_back(poly2[i]);
    }
    multiply(p1,p2,ans);
    for (int i = 0; i < ans.size(); ++i)
    {
        int pos = l + sz + i;
        poly2[pos] = (poly2[pos] + ans[i])%MOD;
    }
}
int main()
{
    fact[0] = invfact[0] = pow2[0] = all_graphs[0] = 1;
    for (int i = 1; i < MAXN; ++i)
    {
        fact[i] = (fact[i-1]*i)%MOD;
        invfact[i] = power(fact[i], MOD-2);
        pow2[i] = (pow2[i-1]*2)%MOD;
        all_graphs[i] = (all_graphs[i-1]*pow2[i-1])%MOD;
        poly1[i] = (all_graphs[i]*invfact[i])%MOD;
    }
    dnc(1,(1<<17)+1);
    int t;
    cin>>t;
    while(t--)
    {
        int x;
        cin>>x;
        cout<<(poly2[x]*fact[x-1])%MOD<<"\n";
    }
    return 0;
}

{"mode":"full","isActive":false}


Problem solution in C.

#include<stdio.h>
#define MAX_N 150000
#define MODULE 663224321
static long long f[MAX_N];
static long long g[MAX_N];
static long long factorial_inverse[MAX_N];
static long long factorial[MAX_N];
static long long x1[MAX_N];
static long long x2[MAX_N];
static long long y[MAX_N];
long long power(long long x, long long n)
{
    long long res = 1;
    for( ; n ; n >>= 1, x = x * x % MODULE )
    {
        if( n & 1 )
        {
            res = ( res * x ) % MODULE;
        }
    }
    return res;
}
void Run(long long *x, long long n, long long rev)
{
    for( long long i = 1, j, k, t ; i < n ; ++i )
    {
        for( j = 0, t = i, k = n >> 1 ; k ; t >>= 1, k >>= 1 )
        {
            j = j << 1 | t & 1;
        }
        if( i < j )
        {
            long long tmp = x[i];
            x[i] = x[j];
            x[j] = tmp;
        }
    }
    for( long long s = 2, ds = 1 ; s <= n ; ds = s, s <<= 1 )
    {
        long long wn = power(3, (MODULE - 1) / s);
        if( rev < 0 )
        {
            wn = power(wn, MODULE - 2);
        }
        for( long long k = 0 ; k < n ; k += s )
        {
            long long w = 1, t;
            for( long long i = k ; i < k + ds ; ++ i, w = w * wn % MODULE )
            {
                x[i+ds] = ( x[i] - ( t = w * x[i+ds] % MODULE ) + MODULE ) % MODULE;
                x[i] = ( x[i] + t ) % MODULE;
            }
        }
    }
    if( rev < 0 )
    {
        long long invn = power(n, MODULE - 2);
        for( long long i = 0 ; i < n ; ++i )
        {
            x[i] = x[i] * invn % MODULE;
        }
    }
}
void divide_conquer(long long left, long long right)
{
    if( left == right )
    {
        return;
    }
    long long mid = ( left + right ) / 2;
    divide_conquer(left, mid);
    long long n1;
    for( n1 = 1 ; n1 <= right - left ; n1 <<= 1 );
    for( long long i = 0 ; i < n1 ; ++i )
    {
        x1[i] = ( i + left <= mid ) ? f[i+left] * factorial_inverse[i+left-1] % MODULE : 0;
        x2[i] = (i + left <= right) ? factorial_inverse[i+1] * g[i+1] % MODULE : 0;
    }
    Run(x1, n1, 1);
    Run(x2, n1, 1);
    for( long long i = 0 ; i < n1 ; ++i )
    {
        y[i] = x1[i] * x2[i] % MODULE;
    }
    Run(y, n1, -1);
    for( long long i = mid + 1 ; i <= right ; ++i )
    {
        f[i] = ( f[i] - ( factorial[i-1] * y[i-left-1] % MODULE ) + MODULE ) % MODULE;
    }
    divide_conquer(mid + 1, right);
}
void initialize()
{
    factorial[0] = 1;
    factorial_inverse[0] = 1;
    for( long long i = 1 ; i < MAX_N ; ++i )
    {
        factorial[i] = ( factorial[i-1] * i ) % MODULE;
        factorial_inverse[i] = power(factorial[i], MODULE - 2);
        g[i] = power(2, (long long)i * (long long)(i - 1) / 2);
        f[i] = g[i];
    }
    divide_conquer(1, 100000);
}
int main()
{
    int q, n;
    initialize();
    scanf("%d", &q);
    for( long long i = 0 ; i < q ; ++i )
    {
        scanf("%d", &n);
        printf("%lld\n", f[n]);
    }
    return 0;
}

{"mode":"full","isActive":false}