1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158
| #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 = 167772161, inv2 = mod + 1 >> 1; int n, k, 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] = ((LL)p + q) % mod, x[i | j | mid] = ((LL)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); } void PolyExp(int n, int *x, int *g) { if (n == 1) return void(g[0] = 1); int m = n + 1 >> 1; PolyExp(m, x, g); for (int i = m; i < n; ++i) g[i] = 0; static int A[N]; PolyLn(n, g, A); for (int i = 0; i < n; ++i) A[i] = ((LL)x[i] - A[i]) % mod; ++A[0]; PolyMul(n, A, m, g, n, g); } void PolyBinpow(int n, int *x, int k, int *g) { static int A[N], B[N]; int t = 0; while (t < n && !x[t]) ++t; if ((LL)k * t >= n) { for (int i = 0; i < n; ++i) g[i] = 0; return; } int s = binpow(x[t]); for (int i = 0; i < n - t; ++i) A[i] = (LL)x[i + t] * s % mod; PolyLn(n - t, A, B); for (int i = 0; i < n - t; ++i) B[i] = (LL)B[i] * k % mod; PolyExp(n - t, B, g); s = binpow(x[t], k); for (int i = n - 1; i >= k * t; --i) g[i] = (LL)g[i - k * t] * s % mod; for (int i = 0; i < k * t; ++i) g[i] = 0; } int main () { static int n, m, A[N], B[N]; read(n, m); ++n; (++A[1]) %= mod; PolyExp(n, A, B); (--B[0]) %= mod; PolyBinpow(n, B, m, A); int k = 1; for (int i = 2; i <= m; ++i) k = (LL)k * i % mod; k = binpow(k); for (int i = 0, t = 1; i < n; t = (LL)t * ++i % mod) write(((LL)A[i] * k % mod * t % mod + mod) % mod), putchar(' '); return 0; }
|