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NTT， 求逆，积分微分，对数指数，快速幂，除法。

查看代码 
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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 = 998244353, 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 PolySqrt(int n, int *x, int *g)
{
    if (n == 1) return void(g[0] = 1);
    int m = n + 1 >> 1;
    int bit = 0;
    while (1 << bit < n + n - 1) ++bit;
    int tot = 1 << bit;
    PolySqrt(m, x, g);
    for (int i = m; i < n; ++i) g[i] = 0;
    static int A[N], B[N];
    PolyInv(n, g, A);
    for (int i = n; i < tot; ++i) A[i] = 0;
    for (int i = 0; i < tot; ++i) B[i] = x[i];
    for (int i = n; i < tot; ++i) B[i] = 0;
    ntt(A, bit, 1), ntt(B, bit, 1), ntt(g, bit, 1);
    for (int i = 0; i < tot; ++i)
        g[i] = (g[i] + (LL)B[i] * A[i]) % mod * inv2 % 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] = (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;
}
void PolyDiv(int n, int *x, int m, int *y, int *c, int *r)
{
    int del = n - m + 1;
    static int A[N], B[N];
    for (int i = 0; i < m; ++i) B[i] = y[m - i - 1];
    PolyInv(del, B, A);
    for (int i = 0; i < n; ++i) B[i] = x[n - i - 1];
    PolyMul(del, A, n, B, del, A);
    for (int i = 0; i < del; ++i)
        c[i] = A[del - i - 1];
    for (int i = 0; i < del; ++i) A[i] = c[i];
    for (int i = 0; i < m; ++i) B[i] = y[i];
    PolyMul(del, A, m, B, n, A);
    for (int i = 0; i < n; ++i)
        r[i] = (x[i] - A[i]) % mod;
}

三模数NTT：

查看代码 
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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')
        c == '-' && (flag = true);
    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(x % 10 + '0');
}
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;
}
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]);
}
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