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| #include <cstdio> #include <vector> 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 = 3e6 + 10; int w, iw, mod, g[2][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 init () { vector <int> p; auto check = [&](int k) { for (int i : p) if (binpow(k, (mod - 1) / i) == 1) return false; return true; }; int x = mod - 1; for (int i = 2; i * i <= x; ++i) if (x % i == 0) { p.push_back(i); while (x % i == 0) x /= i; } if (x > 1) p.push_back(x); for (int i = 2; i < mod; ++i) if (check(i)) { w = i; break; } iw = binpow(w); g[0][0] = g[1][0] = 1; for (int i = 1, t = 1, it = 1; i < mod << 1; ++i, t = (LL)t * w % mod, it = (LL)it * iw % mod) g[0][i] = (LL)g[0][i - 1] * t % mod, g[1][i] = (LL)g[1][i - 1] * it % mod; } namespace Poly { const LL mod = 180143985094819841; int rev[N]; LL binpow (LL b, LL k = mod - 2) { LL res = 1; for (; k; k >>= 1, b = (L)b * b % mod) if (k & 1) res = (L)res * b % mod; return res; } void ntt (LL *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) { LL w1 = binpow(6, (mod - 1) / (mid << 1)); if (!~op) w1 = binpow(w1); for (int i = 0; i < tot; i += mid << 1) { LL k = 1; for (int j = 0; j < mid; ++j, k = (L)k * w1 % mod) { LL p = x[i | j], q = (L)k * x[i | j | mid] % mod; x[i | j] = (p + q) % mod, x[i | j | mid] = (p - q) % mod; } } } if (~op) return; LL itot = binpow(tot); for (int i = 0; i < tot; ++i) x[i] = (L)x[i] * itot % mod; } void PolyMul (int n, LL *f, int m, LL *g, int nm, LL *res) { int bit = 0; while (1 << bit < max(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] = (L)f[i] * g[i] % mod; ntt(res, bit, -1); for (int i = 0; i < nm; ++i) if (res[i] < 0) res[i] += mod; for (int i = nm; i < tot; ++i) res[i] = 0; } } void BlueStein (int *x, int n, int op) { static LL A[N], B[N]; for (int i = 0; i < n; ++i) A[i] = (LL)x[i] * g[op ^ 1][i] % mod; for (int i = 0; i < n + n - 1; ++i) B[n + n - 2 - i] = g[op][i]; Poly::PolyMul(n, A, n + n - 1, B, n + n - 1, A); for (int i = 0; i < n; ++i) x[i] = A[n + n - 2 - i] % mod * g[op ^ 1][i] % mod; if (!op) return; int itot = binpow(n); for (int i = 0; i < n; ++i) x[i] = (LL)x[i] * itot % mod; } int main () { static int n, c, A[N], B[N]; read(n, c); mod = n + 1; init(); for (int i = 0; i < n; ++i) read(A[i]); for (int i = 0; i < n; ++i) read(B[i]); BlueStein(A, n, 0), BlueStein(B, n, 0); for (int i = 0; i < n; ++i) A[i] = (LL)A[i] * binpow(B[i], c) % mod; BlueStein(A, n, 1); for (int i = 0; i < n; ++i) write((A[i] + mod) % mod), puts(""); return 0; }
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