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181 | #include<bits/stdc++.h>
#define up(l, r, i) for(int i = l, END##i = r;i <= END##i;++ i)
#define dn(r, l, i) for(int i = r, END##i = l;i >= END##i;-- i)
using namespace std;
using i64 = long long;
const int INF = 1e9;
const i64 INFL = 1e18;
const int MOD = 998244353;
int power(int a, int b){
int r = 1;
while(b){
if(b & 1) r = 1ll * r * a % MOD;
b >>= 1, a = 1ll * a * a % MOD;
}
return r;
}
int inv(int x){
return power(x, MOD - 2);
}
const int MAX_ = (1 << 19) + 3;
struct cplx{
double a, b; cplx(double _a = 0, double _b = 0) :a(_a), b(_b){}
cplx operator +(cplx t){ return cplx(a + t.a, b + t.b); }
cplx operator -(cplx t){ return cplx(a - t.a, b - t.b); }
cplx operator *(cplx t){ return cplx(a * t.a - b * t.b, a * t.b + b * t.a); }
cplx operator *(int t) { return cplx(a * t, b * t); }
};
const long double pi = acos(-1);
namespace Poly{
void FFT(int n, cplx Z[]){
static int W[MAX_];
int l = 1; W[0] = 0;
while (n >>= 1)
up(0, l - 1, i)
W[l++] = W[i] << 1 | 1, W[i] <<= 1;
up(0, l - 1, i)
if(W[i] > i) swap(Z[i], Z[W[i]]);
for (n = l >> 1, l = 1;n;n >>= 1, l <<= 1){
cplx* S = Z, o(cos(pi / l), sin(pi / l));
up(0, n - 1, i){
cplx s(1, 0);
up(0, l - 1, j){
cplx x = S[j] + s * S[j + l];
cplx y = S[j] - s * S[j + l];
S[j] = x, S[j + l] = y, s = s * o;
}
S += l << 1;
}
}
}
void IFFT(int n, cplx Z[]){
FFT(n, Z); reverse(Z + 1, Z + n);
up(0, n - 1, i)
Z[i].a /= 1.0 * n, Z[i].b /= 1.0 * n;
}
void NTT(int n, int Z[]){
static int W[MAX_];
int g = 3, l = 1;
W[0] = 0;
while (n >>= 1)
up(0, l - 1, i)
W[l++] = W[i] << 1 | 1, W[i] <<= 1;
up(0, l - 1, i)
if (W[i] > i)swap(Z[i], Z[W[i]]);
for (n = l >> 1, l = 1;n;n >>= 1, l <<= 1){
int* S = Z, o = power(g, (MOD - 1) / l / 2);
up(0, n - 1, i){
int s = 1;
up(0, l - 1, j){
int x = (S[j] + 1ll * s * S[j + l] % MOD ) % MOD;
int y = (S[j] - 1ll * s * S[j + l] % MOD + MOD) % MOD;
S[j] = x, S[j + l] = y;
s = 1ll * s * o % MOD;
}
S += l << 1;
}
}
}
void INTT(int n, int Z[]){
NTT(n, Z); reverse(Z + 1, Z + n);
int o = inv(n);
up(0, n - 1, i)
Z[i] = 1ll * Z[i] * o % MOD;
}
void MUL(int n, int A[], int B[]){ // 乘法
NTT(n, A), NTT(n, B);
up(0, n - 1, i)
A[i] = 1ll * A[i] * B[i] % MOD;
INTT(n, A);
}
void INV(int n, int Z[], int T[]){ // 乘法逆
static int A[MAX_];
up(0, n - 1, i)
T[i] = 0;
T[0] = power(Z[0], MOD - 2);
for (int l = 1;l < n;l <<= 1){
up( 0, 2 * l - 1, i) A[i] = Z[i];
up(2 * l, 4 * l - 1, i) A[i] = 0;
NTT(4 * l, A), NTT(4 * l, T);
up(0, 4 * l - 1, i)
T[i] = (2ll * T[i] - 1ll * A[i] * T[i] % MOD * T[i] % MOD + MOD) % MOD;
INTT(4 * l, T);
up(2 * l, 4 * l - 1, i)
T[i] = 0;
}
}
void DIF(int n, int Z[], int T[]){ // 微分
up(0, n - 2, i)
T[i] = 1ll * Z[i + 1] * (i + 1) % MOD;
T[n - 1] = 0;
}
void INT(int n, int c, int Z[], int T[]){ // 积分
up(1, n - 1, i)
T[i] = 1ll * Z[i - 1] * inv(i) % MOD;
T[0] = c;
}
void LN(int n, int* Z, int* T){ // 求对数
static int A[MAX_];
static int B[MAX_];
up(0, 2 * n - 1, i)
A[i] = B[i] = 0;
DIF(n, Z, A);
INV(n, Z, B);
MUL(2 * n, A, B);
INT(n, 0, A, T);
}
void EXP(int n, int* Z, int* T){ // 求指数
static int A[MAX_];
static int B[MAX_];
up(1, 2 * n - 1, i) T[i] = 0;
T[0] = 1;
for (int l = 1;l < n;l <<= 1){
LN (2 * l, T, A);
up( 0, 2 * l - 1, i)
B[i] = (-A[i] + Z[i] + MOD) % MOD;
B[0] = (B[0] + 1) % MOD;
up(2 * l, 4 * l - 1, i)
T[i] = B[i] = 0;
MUL(4 * l, T, B);
}
}
void SQT(int n, int* Z, int* T){ // 开根
static int A[MAX_];
static int B[MAX_];
up(1, 2 * n - 1, i) T[i] = 0;
T[0] = 1;
int o = inv(2);
for (int l = 1;l < n;l <<= 1){
INV(2 * l, T, A);
up(0, 2 * l - 1, i)
B[i] = Z[i];
up(2 * l, 4 * l - 1, i)
A[i] = B[i] = 0;
MUL(4 * l, A, B);
up(0, 2 * l - 1, i)
T[i] = 1ll * (T[i] + A[i]) * o % MOD;
}
}
void SHF(int n, int c, int* Z, int* T){ // 平移
static int A[MAX_];
static int B[MAX_];
static int F[MAX_];
static int G[MAX_];
int o = 1;
up(1, n - 1, i)
F[i] = 1ll * F[i - 1] * i % MOD,
G[i] = 1ll * G[i - 1] * inv(i) % MOD;
up(0, n - 1, i)
A[i] = 1ll * Z[n - 1 - i] * F[n - 1 - i] % MOD;
up(0, n - 1, i){
B[i] = 1ll * G[i] * o % MOD;
o = 1ll * o * c % MOD;
}
int l = 1; while (l < 2 * n - 1) l <<= 1;
up(n, l - 1, i)
A[i] = B[i] = 0;
MUL(l, A, B);
up(0, n - 1, i)
T[n - 1 - i] = 1ll * G[n - 1 - i] * A[i] % MOD;
}
}
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