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| #include <cstdio> #include <algorithm> using namespace std; template <class Type> void read (Type &x) { char c; bool flag = false; while ((c = getchar()) < '0' || c > '9') flag |= c == '-'; x = c - '0'; while ((c = getchar()) >= '0' && c <= '9') x = (x << 3) + (x << 1) + c - '0'; if (flag) x = ~x + 1; } template <class Type, class ...Rest> void read (Type &x, Rest &...y) { read(x); read(y...); } template <class Type> void write (Type x) { if (x < 0) putchar('-'), x = ~x + 1; if (x > 9) write(x / 10); putchar('0' + x % 10); } typedef long long LL; const int N = 5e5 + 10, mod = 1004535809, inv2 = mod + 1 >> 1; int rev[N]; int binpow (int b, int k = mod - 2) { int res = 1; for (; k; k >>= 1, b = (LL)b * b % mod) if (k & 1) res = (LL)res * b % mod; return res; } void ntt (int *x, int bit, int op) { int tot = 1 << bit; for (int i = 1; i < tot; ++i) if ((rev[i] = rev[i >> 1] >> 1 | (i & 1) << bit - 1) > i) swap(x[rev[i]], x[i]); for (int mid = 1; mid < tot; mid <<= 1) { int w1 = binpow(3, (mod - 1) / (mid << 1)); if (!~op) w1 = binpow(w1); for (int i = 0; i < tot; i += mid << 1) for (int j = 0, k = 1; j < mid; ++j, k = (LL)k * w1 % mod) { int p = x[i | j], q = (LL)k * x[i | j | mid] % mod; x[i | j] = (p + q) % mod, x[i | j | mid] = (p - q) % mod; } } if (~op) return; int itot = binpow(tot); for (int i = 0; i < tot; ++i) x[i] = (LL)x[i] * itot % mod; } void PolyMul (int n, int *f, int m, int *g, int nm, int *res) { int bit = 0; while (1 << bit < n + m - 1) ++bit; int tot = 1 << bit; for (int i = n; i < tot; ++i) f[i] = 0; for (int i = m; i < tot; ++i) g[i] = 0; ntt(f, bit, 1), ntt(g, bit, 1); for (int i = 0; i < tot; ++i) res[i] = (LL)f[i] * g[i] % mod; ntt(res, bit, -1); for (int i = nm; i < tot; ++i) res[i] = 0; } void PolyInv(int n, int *x, int *g) { if (n == 1) return void(g[0] = binpow(x[0])); int m = n + 1 >> 1; int bit = 0; while (1 << bit < n + m + m - 2) ++bit; int tot = 1 << bit; PolyInv(m, x, g); for (int i = m; i < tot; ++i) g[i] = 0; static int A[N]; for (int i = 0; i < n; ++i) A[i] = x[i]; for (int i = n; i < tot; ++i) A[i] = 0; ntt(g, bit, 1), ntt(A, bit, 1); for (int i = 0; i < tot; ++i) g[i] = (2 - (LL)g[i] * A[i]) % mod * g[i] % mod; ntt(g, bit, -1); for (int i = n; i < tot; ++i) g[i] = 0; } void PolyDerivate(int n, int *x, int *g) { for (int i = 1; i < n; ++i) g[i - 1] = (LL)x[i] * i % mod; g[n - 1] = 0; } void PolyIntegrate(int n, int *x, int *g) { for (int i = 1; i < n; ++i) g[i] = (LL)x[i - 1] * binpow(i) % mod; g[0] = 0; } void PolyLn(int n, int *x, int *g) { static int A[N], B[N]; PolyDerivate(n, x, A); PolyInv(n, x, B); PolyMul(n, A, n, B, n, A); PolyIntegrate(n, A, g); } int main () { static int n, A[N], B[N]; read(n); for (int i = 0, t = 1; i <= n; t = (LL)t * ++i % mod) A[i] = (LL)binpow(t) * binpow(2, i * (i - 1ll) / 2 % (mod - 1)) % mod; PolyLn(n + 1, A, B); int k = 1; for (int i = 2; i <= n; ++i) k = (LL)k * i % mod; write(((LL)k * B[n] % mod + mod) % mod); return 0; }
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