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| const int MAXN = 1 << 20;
const int MOD = 998244353;
namespace polynomial {
inline int add(int x, int y) { return x += y, x >= MOD ? x - MOD : x; }
inline int sub(int x, int y) { return x -= y, x < 0 ? x + MOD : x; }
inline int qpow(int x, int y, int p = MOD) {
int ret = 1;
for (; y; y >>= 1, x = 1ll * x * x % p)
if (y & 1) ret = 1ll * ret * x % p;
return ret;
}
template <class _Tp>
void change(_Tp* f, int len) {
static int rev[MAXN] = {};
for (int i = rev[0] = 0; i < len; ++i) {
rev[i] = rev[i >> 1] >> 1;
if (i & 1) rev[i] |= len >> 1;
}
for (int i = 0; i < len; ++i)
if (i < rev[i]) swap(f[i], f[rev[i]]);
}
void ntt(int* f, int len, int on) {
change(f, len);
for (int h = 2; h <= len; h <<= 1) {
int gn = qpow(3, (MOD - 1) / h);
for (int j = 0; j < len; j += h) {
int g = 1;
for (int k = j; k < j + h / 2; ++k) {
int u = f[k], t = 1ll * g * f[k + h / 2] % MOD;
f[k] = add(u, t), f[k + h / 2] = sub(u, t);
g = 1ll * g * gn % MOD;
}
}
}
if (on == -1) {
reverse(f + 1, f + len);
int inv = qpow(len, MOD - 2);
for (int i = 0; i < len; ++i) f[i] = 1ll * f[i] * inv % MOD;
}
}
int polymul(const int* f, int n, const int* g, int m, int* ans) {
static int tf[MAXN] = {}, tg[MAXN] = {};
int len = 1;
while (len < n + m - 1) len <<= 1;
copy(f, f + n, tf), fill(tf + n, tf + len, 0);
copy(g, g + m, tg), fill(tg + m, tg + len, 0);
ntt(tf, len, 1), ntt(tg, len, 1);
for (int i = 0; i < len; ++i) tf[i] = 1ll * tf[i] * tg[i] % MOD;
ntt(tf, len, -1);
copy(tf, tf + n + m - 1, ans);
return n + m - 1;
}
int polyinv(const int* f, int n, int* ans) {
static int tmp[MAXN] = {};
int len = 1;
while (len < n) len <<= 1;
fill(ans, ans + len + len, 0);
ans[0] = qpow(f[0], MOD - 2);
for (int h = 2; h <= len; h <<= 1) {
copy(f, f + h, tmp);
fill(tmp + h, tmp + h + h, 0);
ntt(tmp, h + h, 1), ntt(ans, h + h, 1);
for (int i = 0; i < h + h; ++i)
ans[i] = 1ll * ans[i] * (2 - 1ll * ans[i] * tmp[i] % MOD + MOD) % MOD;
ntt(ans, h + h, -1), fill(ans + h, ans + h + h, 0);
}
return n;
}
int derivation(const int* f, int n, int* ans) {
for (int i = 0; i < n - 1; ++i)
ans[i] = 1ll * f[i + 1] * (i + 1) % MOD;
return ans[n - 1] = 0, n - 1;
}
int integral(const int* f, int n, int* ans) {
for (int i = n; i >= 1; --i)
ans[i] = 1ll * f[i - 1] * qpow(i, MOD - 2) % MOD;
return ans[0] = 0, n + 1;
}
int ln(const int* f, int n, int* ans) {
static int tf[MAXN] = {}, tg[MAXN] = {};
derivation(f, n, tf);
polyinv(f, n, tg);
polymul(tf, n - 1, tg, n, ans);
integral(ans, n - 1, ans);
fill(ans + n, ans + n + n, 0);
return n;
}
int exp(const int* f, int n, int* ans) {
static int tmp[MAXN] = {};
ans[0] = 1, ans[1] = 0;
for (int h = 2; h <= (n << 1); h <<= 1) {
ln(ans, h, tmp);
for (int i = 0; i < h; ++i)
tmp[i] = add(i == 0, sub(f[i], tmp[i]));
polymul(ans, h, tmp, h, ans);
}
return n;
}
};
using namespace polynomial;
|