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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 __int128 L; typedef long long LL; const int N = 5e5 + 10, p = 1e9 + 7, p1 = 998244353, p2 = 1004535809, p3 = 469762049; const L inf = (L)N * p * p, mul = (L)p1 * p2 * p3; int binpow (int b, int k = p - 2) { int res = 1; for (; k; k >>= 1, b = (LL)b * b % p) if (k & 1) res = (LL)res * b % p; return res; } int fact[N], ifact[N]; template <const int &mod> struct NTT { 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 = 0; 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 *w) { static int A[N], B[N]; for (int i = 0; i < n; ++i) A[i] = f[i] % mod; for (int i = 0; i < m; ++i) B[i] = g[i] % mod; int bit = 1; while (n + m - 1 > 1 << bit) ++bit; int tot = 1 << bit; for (int i = n; i < tot; ++i) A[i] = 0; for (int i = m; i < tot; ++i) B[i] = 0; ntt(A, bit, 1), ntt(B, bit, 1); for (int i = 0; i < tot; ++i) w[i] = (LL)A[i] * B[i] % mod; ntt(w, bit, -1); for (int i = 0; i < nm; ++i) w[i] = (w[i] + mod) % mod; for (int i = nm; i < tot; ++i) w[i] = 0; } }; NTT <p1> q1; NTT <p2> q2; NTT <p3> q3; const L k1 = (L)p2 * p3 * q1.binpow((LL)p2 * p3 % p1), k2 = (L)p1 * p3 * q2.binpow((LL)p1 * p3 % p2), k3 = (L)p1 * p2 * q3.binpow((LL)p1 * p2 % p3); int CRT (int x1, int x2, int x3) { L res = (x1 * k1 + x2 * k2 + x3 * k3) % mul; if (res >= inf) res -= mul; if (res <= -inf) res += mul; return res % p; } void PolyMul (int n, int *f, int m, int *g, int nm, int *w) { static int A[N], B[N], C[N]; q1.PolyMul(n, f, m, g, nm, A); q2.PolyMul(n, f, m, g, nm, B); q3.PolyMul(n, f, m, g, nm, C); for (int i = 0; i < nm; ++i) w[i] = CRT(A[i], B[i], C[i]); } void PolyCalc (int n, LL m, int *g) { if (m == 1) { for (int i = 1; i < n; ++i) g[i] = 1; return; } PolyCalc(n, m >> 1, g); static int A[N], B[N]; A[0] = B[0] = 0; for (int i = 1, s = binpow(2, (m >> 1) % (p - 1)), t = s; i < n; ++i, t = (LL)t * s % p) { A[i] = (LL)g[i] * t % p * ifact[i] % p; B[i] = (LL)g[i] * ifact[i] % p; } PolyMul(n, A, n, B, n, A); for (int i = 1; i < n; ++i) g[i] = (LL)A[i] * fact[i] % p; if (!(m & 1)) return; A[0] = B[0] = 0; for (int i = 1; i < n; ++i) { A[i] = (LL)g[i] * binpow(2, i) % p * ifact[i] % p; B[i] = ifact[i]; } PolyMul(n, A, n, B, n, A); for (int i = 1; i < n; ++i) g[i] = (LL)A[i] * fact[i] % p; } void init () { fact[0] = 1; for (int i = 1; i < N; ++i) fact[i] = (LL)fact[i - 1] * i % p; ifact[N - 1] = binpow(fact[N - 1]); for (int i = N - 1; i; --i) ifact[i - 1] = (LL)ifact[i] * i % p; } int main () { init(); LL n; int m; static int A[N]; read(n, m); PolyCalc(m + 1, n, A); int res = 0; for (int i = 1; i <= m; ++i) res = (res + (LL)A[i] * ifact[i] % p * ifact[m - i]) % p; write(((LL)res * fact[m] % p + p) % p); return 0; }
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