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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;
}
|