mirror of
https://github.com/Kiritow/OJ-Problems-Source.git
synced 2024-03-22 13:11:29 +08:00
127 lines
3.2 KiB
C++
127 lines
3.2 KiB
C++
#include <cstdio>
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#include <cstring>
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#include <algorithm>
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#include <iostream>
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#include <cmath>
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#include <map>
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#include <vector>
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#include <stack>
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using namespace std;
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#define mod 1004535809LL
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#define G 3LL
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#define maxn 455555
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long long x1[maxn], x2[maxn];
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long long qpow (long long a, long long b) {
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long long ret=1;
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while (b) {
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if (b&1) ret = (ret*a)%mod;
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a = (a*a)%mod;
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b >>= 1;
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}
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return ret;
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}
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void change (long long *y, int len) {
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int i, j, k;
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for(i = 1, j = len / 2; i < len - 1; i++) {
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if (i < j) swap(y[i], y[j]);
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k = len / 2;
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while (j >= k) {
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j -= k;
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k /= 2;
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}
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if (j < k) j += k;
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}
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}
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void ntt (long long *y, int len, int on) {
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change (y, len);
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int id = 0;
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for(int h = 2; h <= len; h <<= 1) {
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id++;
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long long wn = qpow (G, (mod - 1) / (1<<id));
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for(int j = 0; j < len; j += h) {
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long long w = 1;
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for(int k = j; k < j + h / 2; k++) {
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long long u = y[k] % mod;
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long long t = w * (y[k + h / 2] % mod) % mod;
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y[k] = (u + t) % mod;
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y[k + h / 2] = ((u - t) % mod + mod) % mod;
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w = w * wn % mod;
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}
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}
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}
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if (on == -1) {
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for (int i = 1; i < len / 2; i++)
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swap (y[i], y[len - i]);
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long long inv = qpow(len, mod - 2);
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for(int i = 0; i < len; i++)
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y[i] = y[i] % mod * inv % mod;
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}
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}
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long long n, m;
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long long f[maxn], g[maxn], h[maxn];
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//n个点的有环图 n个点的图 n个点的树
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long long fac[maxn], rev[maxn];
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void solve (int l, int r) { //cout << l << " " << r << endl;
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if (l == r) {
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f[l] += h[l];
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f[l] %= mod;
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return;
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}
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int mid = (l+r) >> 1;
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solve (l, mid);
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int len = 1;
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while (len <= r-l+1) {len <<= 1;}
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for (int i = 0; i < len; i++) {
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x1[i] = x2[i] = 0;
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}
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for (int i = l; i <= mid; i++) {
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x1[i-l] = f[i]*rev[i]%mod;
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}
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for (int i = 1; i <= r-l; i++) {
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x2[i-1] = h[i]*rev[i-1]%mod;
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}
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ntt (x1, len, 1), ntt (x2, len, 1);
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for (int i = 0; i < len; i++) x1[i] = x1[i] * x2[i] % mod;
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ntt (x1, len, -1);
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for (int i = mid+1; i <= r; i++) {
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f[i] += x1[i-l-1]*fac[i-1] %mod;
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f[i] %= mod;
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}
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//cout << l << " " << r << endl;
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//for (int i = 1; i <= 4; i++) cout << f[i] << " "; cout << endl;
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solve (mid+1, r);
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}
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int main () {
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// freopen ("in", "r", stdin);
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// freopen ("out", "w", stdout);
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// //int t1 = clock ();
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g[1] = h[1] = 1;
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for (int i = 2; i <= 200000; i++) {
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h[i] = qpow (i, i-2);
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g[i] = qpow (2, 1LL*i*(i-1)/2);
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}
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fac[0] = 1;
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for (int i = 1; i <= 200000; i++) fac[i] = fac[i-1] * i % mod;
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rev[200000] = qpow (fac[200000], mod - 2);
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for (int i = 200000-1; i >= 0; i--) rev[i] = rev[i+1] * (i+1) % mod;
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int t;
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scanf ("%d", &t);
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while (t--) {
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scanf ("%lld", &n);
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memset (f, 0, sizeof f);
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solve (1, n);
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long long ans = g[n]-f[n];
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(ans %= mod) += mod; ans %= mod;
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printf ("%lld\n", ans);
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}
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//int t2 = clock ();
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//cout << t2-t1 << endl;
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return 0;
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}
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