尝试强行记忆，尝试失败。。。
把最终所有的式子写一遍。
约定 \(F^{*}(x)\) 表示 \(\pmod{x^{n/2}}\) 意义下的结果，\(F^{R}(x)\) 表示系数翻转。
\(\mathtt{Summary}\)
\(\mathtt{Poly \ INV}\)
\[G(0)= F(0)' \\
G(x) = G^{*}(x)(2 - F(x)G^{*}(x))
\]
\(\mathtt{Poly \ Sqrt}\)
\[G(0) = \sqrt{F(0)} \\
G(x) = \frac{F(x) + G^{*}(x)^2}{2G^{*}(x)}
\]
\(\mathtt{Poly \ Div}\)
\[F^{R}(x) = Q^{R}(x)G^{R}(x) \pmod{x^{n - m - 1}}
\]
\(\mathtt{Poly \ ln}\)
\[G(0) = 0 \\
\frac{F'(x)}{F(x)} = G(x)
\]
\(\mathtt{Poly \ exp}\)
\[G(0) = 1 \\
G(x)=(1 - \ln B^{*}(x) + A(x))B^{*}(x)
\]
\(\mathtt{Poly \ quickpower}\)
\[F^{k}(x) = e^{\ln(F(x)) \times k}
\]
\(\mathtt{Code}\)
namespace Poly {
const int Mod = 998244353;
const int rt = 3;
int lim, l, cnt, r[MAXN];
LL a[MAXN], b[MAXN], c[MAXN], d[MAXN], tmp[MAXN];
LL qpow(LL x, int y) { LL res = 1; while (y) { if (y & 1) res = res * x % Mod; x = x * x % Mod, y >>= 1; } return res; }
void init(int deg) {
lim = 1, l = 0;
while (lim < deg) lim <<= 1, l++;
for (int i = 1; i < lim; i++) r[i] = (r[i >> 1] >> 1) | ((i & 1) << (l - 1));
}
void ntt(LL* arr, int type) {
for (int i = 0; i < lim; i++) if (i < r[i]) swap(arr[i], arr[r[i]]);
for (int mid = 1; mid < lim; mid <<= 1) {
LL w = qpow(rt, type == 1 ? (Mod - 1) / (mid << 1) : (Mod - 1) - (Mod - 1) / (mid << 1));
for (int pos = mid << 1, j = 0; j < lim; j += pos) {
LL now = 1;
for (int k = 0; k < mid; k++, now = now * w % Mod) {
LL x = arr[k + j], y = now * arr[k + j + mid] % Mod;
arr[k + j] = (x + y) % Mod, arr[k + j + mid] = (x - y + Mod) % Mod;
}
}
}
if (type == -1) { LL inv = qpow(lim, Mod - 2); for (int i = 0; i < lim; i++) arr[i] = arr[i] * inv % Mod; }
}
void PolyMul(int deg, LL* f, LL* g) {
init(deg << 1);
ntt(f, 1), ntt(g, 1);
for (int i = 0; i < lim; i++) f[i] = f[i] * g[i] % Mod;
ntt(f, -1);
for (int i = deg; i <= lim; i++) f[i] = 0;
}
void PolyInv(int deg, LL* f, LL* g) {
if (deg == 1) { g[0] = qpow(f[0], Mod - 2); return; }
PolyInv((deg + 1) >> 1, f, g);
init(deg << 1);
for (int i = 0; i < deg; i++) tmp[i] = f[i];
for (int i = deg; i < lim; i++) tmp[i] = 0;
ntt(tmp, 1), ntt(g, 1);
for (int i = 0; i < lim; i++) g[i] = g[i] * (2 - g[i] * tmp[i] % Mod + Mod) % Mod;
ntt(g, -1);
for (int i = deg; i < lim; i++) g[i] = 0;
}
void PolySW(int deg, LL* f, LL* g) {
if (deg == 1) { g[0] = 1; return; }
memset(b, 0, sizeof(b)), memset(c, 0, sizeof(c)), memset(d, 0, sizeof(d));
PolySW((deg + 1) >> 1, f, g);
for (int i = 0; i < deg; i++) c[i] = g[i] * 2 % Mod, d[i] = g[i], b[i] = 0;
PolyInv(deg, c, b);
PolyMul(deg, g, d);
for (int i = 0; i < deg; i++) g[i] = (g[i] + f[i]) % Mod;
PolyMul(deg, g, b);
}
void PolySqrt(int deg, LL* f, LL* g) {
int cnt = 1; while (cnt <= deg) cnt <<= 1;
PolySW(cnt, f, g);
}
void PolyDev(int deg, LL* f, LL* g) {
for (int i = 1; i < deg; i++) g[i - 1] = i * f[i] % Mod;
g[deg - 1] = 0;
}
void PolyInvDev(int deg, LL*f, LL* g) {
for (int i = 1; i < deg; i++) g[i] = f[i - 1] * qpow(i, Mod - 2) % Mod;
g[0] = 0;
}
void Polyln(int deg, LL* f, LL* g) {
memset(a, 0, sizeof(a)), memset(b, 0, sizeof(b));
PolyDev(deg, f, a), PolyInv(deg, f, b);
PolyMul(deg, a, b);
PolyInvDev(deg, a, g);
}
void PolyExp(int deg, LL* f, LL* g) {
if (deg == 1) { g[0] = 1; return; }
PolyExp((deg + 1) >> 1, f, g);
Polyln(deg, g, d);
init(deg << 1);
for (int i = 0; i < deg; i++) c[i] = f[i];
for (int i = deg; i < lim; i++) c[i] = d[i] = 0;
for (int i = 0; i < lim; i++) c[i] = (c[i] - d[i] + Mod) % Mod;
c[0]++;
ntt(g, 1), ntt(c, 1);
for (int i = 0; i < lim; i++) g[i] = g[i] * c[i] % Mod;
ntt(g, -1);
for (int i = deg; i < lim; i++) g[i] = 0;
return;
}
}