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| namespace Poly
{
#define ll long long
#define poly vector <ll>
const int N = 4e5 + 10;
const int mod = 998244353;
const int g = 3;
const int gi = 332748118;
const int inv2 = (mod + 1) >> 1;
namespace MOD
{
ll add(ll x, ll y){return x + y >= mod ? x + y - mod : x + y;}
ll dec(ll x, ll y){return x - y < 0 ? x - y + mod : x - y;}
}
using namespace MOD;
namespace IO
{
inline ll read()
{
ll x = 0, f = 1;char ch = getchar();
while(!isdigit(ch)){if(ch == '-')f = -1;ch = getchar();}
while(isdigit(ch)){x =((x << 3ll) + (x << 1ll)) + (ch ^ 48ll);ch = getchar();}
return x * f;
}
inline void write(ll x)
{
char ch[100];int len = 0;
if(x == 0)ch[++len] = '0';
if(x < 0)putchar('-'), x = -x;
while(x != 0){ch[++len] = x % 10ll + '0'; x /= 10ll;}
while(len)putchar(ch[len--]);
}
}
using namespace IO;
int rev[N];
ll p[3][50], fv[N];
inline void read(poly &A, int n)
{
A.resize(n + 1);
for(int i = 0; i <= n; i++)
A[i] = read();
}
inline void print(poly B)
{
for(auto x : B)write(x), putchar(' ');
}
inline ll qpow(ll a, ll b)
{
ll t = 1;
while(b != 0)
{
if(b & 1)t = t * a % mod;
a = a * a % mod; b >>= 1;
}
return t;
}
inline ll inv(ll x)
{
return qpow(x, mod - 2);
}
inline void initfv()
{
fv[1] = 1;
for(ll i = 2; i <=(N - 10) / 4; i++)
fv[i] = fv[mod % i] * (mod - mod / i) % mod;
}
inline void prework()
{
for(int k = 1, i = 1; k < N; k <<= 1, i++)
{
p[0][i] = qpow(g, (mod - 1) / (k << 1));
p[1][i] = qpow(gi, (mod - 1) / (k << 1));
p[2][i] = inv(k << 1);
}
}
inline void init(int n, int m, int &len)
{
len = 1; int cnt = 0;
while(len <= (n + m))len <<= 1, cnt++;
for(int i = 0; i < len; i++)
rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (cnt - 1));
}
inline void NTT(poly &a, int len, int type)
{
for(int i = 0; i < len; i++)
if(i < rev[i])swap(a[i], a[rev[i]]);
for(int k = 1, o = 1; k < len; k <<= 1, o++)
{
ll x = type == 1 ? p[0][o] : p[1][o];
for(int i = 0; i < len; i += k << 1)
{
ll w = 1;
for(int j = 0; j < k; j++)
{
ll y = a[i + j];
ll z = w * a[i + j + k] % mod;
a[i + j] = add(y, z);
a[i + j + k] = dec(y, z);
w = w * x % mod;
}
}
}
if(type == -1)
{
ll iv = p[2][(int)log2(len)];
for(int i = 0; i < len; i++)
a[i] = a[i] * iv % mod;
}
}
inline poly operator + (poly A, poly B)
{
int n = max(A.size(), B.size());
A.resize(n); B.resize(n);
for(int i = 0; i < n; i++)
A[i] = add(A[i], B[i]);
return A;
}
inline poly operator - (poly A, poly B)
{
int n = max(A.size(), B.size());
A.resize(n); B.resize(n);
for(int i = 0; i < n; i++)
A[i] = dec(A[i], B[i]);
return A;
}
inline poly operator * (poly A, poly B)
{
int len, n = A.size() - 1, m = B.size() - 1;
init(n, m, len);
A.resize(len); B.resize(len);
NTT(A, len, 1); NTT(B, len, 1);
for(int i = 0; i < len; i++)
A[i] = A[i] * B[i] % mod;
NTT(A, len, -1); A.resize(n + m + 1);
return A;
}
inline void Divide(int l, int r, poly &F, poly &G)
{
if(l == r)return;
int mid = (l + r) >> 1;
Divide(l, mid, F, G);
int n = mid - l + 1;
int m = r - l + 1;
poly A; A.resize(n);
poly B; B.resize(m);
for(int i = l; i <= mid; i++)
A[i - l] = F[i];
for(int i = 1; i <= r - l; i++)
B[i] = G[i];
A = A * B;
for(int i = mid + 1; i <= r; i++)
F[i] = add(F[i], A[i - l]);
Divide(mid + 1, r, F, G);
}
inline void Inverse(poly &A, poly &B, int n)
{
if(n == 1)return void(B[0] = inv(A[0]));
Inverse(A, B, (n + 1) >> 1);
int len; init(n, n, len);
poly C; C.resize(len); B.resize(len);
for(int i = 0; i < n; i++)C[i] = A[i];
NTT(C, len, 1); NTT(B, len, 1);
for(int i = 0; i < len; i++)
B[i] = dec(2, B[i] * C[i] % mod) * B[i] % mod;
NTT(B, len, -1); B.resize(n);
}
inline void Diff(poly &A, poly &B)
{
int n = A.size() - 1;
B.resize(n);
for(ll i = 1; i <= n; i++)
B[i - 1] = i * A[i] % mod;
}
inline void Integ(poly &A, poly &B)
{
int n = A.size();
B.resize(n + 1);
for(int i = 1; i <= n; i++)
B[i] = A[i - 1] * fv[i] % mod;
B[0] = 0;
}
inline void Ln(poly &A, poly &B)
{
int n = A.size() - 1;
poly F; poly G; G.resize(1);
Diff(A, F); Inverse(A, G, n + 1);
F = F * G;
Integ(F, B); B.resize(n + 1);
}
inline void Exp(poly &A, poly &B, int n)
{
if(n == 1)return void(B[0] = 1);
Exp(A, B, (n + 1) >> 1);
poly G; B.resize(n);
Ln(B, G); G[0] -= 1; B = (A - G) * B;
B.resize(n);
}
inline void Sqrt(poly &A, poly &B, int n)
{
if(n == 1)return void(B[0] = 1);
Sqrt(A, B, (n + 1) >> 1);
int len; init(n, n, len); B.resize(n);
poly G, H; H.resize(1); Inverse(B, H, n);
G.resize(len); H.resize(len); B.resize(len);
for(int i = 0; i < n; i++)G[i] = A[i];
NTT(H, len, 1); NTT(B, len, 1); NTT(G, len, 1);
for(int i = 0; i < len; i++)
B[i] = add(B[i], G[i] * H[i] % mod) * inv2 % mod;
NTT(B, len, -1); B.resize(n);
}
inline void Pow(poly &A, poly &B, ll k)
{
int n = A.size() - 1;
poly C; Ln(A, C);
for(int i = 0; i <= n; i++)
C[i] = C[i] * k % mod;
Exp(C, B, n + 1);
}
inline void Mod(poly &F, poly &G, poly &A, poly &B)
{
poly f = F, g = G, h;
int n = F.size() - 1, m = G.size() - 1;
reverse(f.begin(), f.end());
reverse(g.begin(), g.end());
g.resize(n - m + 1);
h.resize(1); Inverse(g, h, n - m + 1);
A = f * h; A.resize(n - m + 1);
reverse(A.begin(), A.end());
B = F - (A * G); B.resize(m);
}
}
using namespace Poly;
|