题意
\[((1+\ln(1+\frac{1}{\exp \int \frac{1}{\sqrt{F(x)}}}))^k)'\]
sol
放个板子。。。
code
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
using namespace std;
int gi()
{
int x=0,w=1;char ch=getchar();
while ((ch<'0'||ch>'9')&&ch!='-') ch=getchar();
if (ch=='-') w=0,ch=getchar();
while (ch>='0'&&ch<='9') x=(x<<3)+(x<<1)+ch-'0',ch=getchar();
return w?x:-x;
}
const int _ = 3e5+5;
const int mod = 998244353;
int rev[_],inv[_],og[_];
int fastpow(int a,int b)
{
int res=1;
while (b) {if (b&1) res=1ll*res*a%mod;a=1ll*a*a%mod;b>>=1;}
return res;
}
void NTT(int *P,int opt,int n)
{
int len,l=0;
for (len=1;len<n;len<<=1) ++l;--l;
for (int i=0;i<len;++i) rev[i]=(rev[i>>1]>>1)|((i&1)<<l);
for (int i=0;i<len;++i) if (i<rev[i]) swap(P[i],P[rev[i]]);
for (int i=1;i<len;i<<=1)
{
int W=fastpow(3,(mod-1)/(i<<1));
if (opt==-1) W=fastpow(W,mod-2);
og[0]=1;for (int j=1;j<i;++j) og[j]=1ll*og[j-1]*W%mod;
for (int p=i<<1,j=0;j<len;j+=p)
for (int k=0;k<i;++k)
{
int X=P[j+k],Y=1ll*P[j+k+i]*og[k]%mod;
P[j+k]=(X+Y)%mod;P[j+k+i]=(X-Y+mod)%mod;
}
}
if (opt==-1)
for (int i=0,Inv=fastpow(len,mod-2);i<len;++i)
P[i]=1ll*P[i]*Inv%mod;
}
int A[_],B[_];
void GetInv(int *a,int *b,int len)
{
if (len==1) {b[0]=fastpow(a[0],mod-2);return;}
GetInv(a,b,len>>1);
for (int i=0;i<len;++i) A[i]=a[i],B[i]=b[i];
NTT(A,1,len<<1);NTT(B,1,len<<1);
for (int i=0;i<(len<<1);++i) A[i]=1ll*A[i]*B[i]%mod*B[i]%mod;
NTT(A,-1,len<<1);
for (int i=0;i<len;++i) b[i]=((b[i]+b[i])%mod-A[i]+mod)%mod;
for (int i=0;i<(len<<1);++i) A[i]=B[i]=0;
}
int C[_],D[_];
void GetSqrt(int *a,int *b,int len)
{
if (len==1) {b[0]=sqrt(a[0]);return;}
GetSqrt(a,b,len>>1);
for (int i=0;i<len;++i) C[i]=a[i];
GetInv(b,D,len);
NTT(C,1,len<<1);NTT(D,1,len<<1);
for (int i=0;i<(len<<1);++i) D[i]=1ll*D[i]*C[i]%mod;
NTT(D,-1,len<<1);
for (int i=0;i<len;++i) b[i]=1ll*(b[i]+D[i])%mod*inv[2]%mod;
for (int i=0;i<(len<<1);++i) C[i]=D[i]=0;
}
void Dao(int *a,int *b,int len)
{
for (int i=1;i<len;++i) b[i-1]=1ll*i*a[i]%mod;
b[len]=b[len-1]=0;
}
void Jifen(int *a,int *b,int len)
{
for (int i=1;i<len;++i) b[i]=1ll*a[i-1]*inv[i]%mod;
b[0]=0;
}
void Getln(int *a,int *b,int len)
{
int A[_],B[_];
memset(A,0,sizeof(A));memset(B,0,sizeof(B));
Dao(a,A,len);GetInv(a,B,len);
NTT(A,1,len<<1);NTT(B,1,len<<1);
for (int i=0;i<(len<<1);++i) A[i]=1ll*A[i]*B[i]%mod;
NTT(A,-1,len<<1);
Jifen(A,b,len);
}
int E[_];
void GetExp(int *a,int *b,int len)
{
if (len==1) {b[0]=1;return;}
GetExp(a,b,len>>1);
for (int i=0;i<len;++i) D[i]=b[i];
Getln(b,E,len);
for (int i=0;i<len;++i) E[i]=(mod-E[i]+a[i])%mod;E[0]=(E[0]+1)%mod;
NTT(D,1,len<<1);NTT(E,1,len<<1);
for (int i=0;i<(len<<1);++i) D[i]=1ll*D[i]*E[i]%mod;
NTT(D,-1,len<<1);
for (int i=0;i<len;++i) b[i]=D[i];
for (int i=0;i<(len<<1);++i) D[i]=E[i]=0;
}
void GetPow(int *a,int *b,int len,int k)
{
int F[_];memset(F,0,sizeof(F));
Getln(a,F,len);
for (int i=0;i<len;++i) F[i]=1ll*F[i]*k%mod;
GetExp(F,b,len);
}
int X[_],Y[_];
int main()
{
freopen("polynomial.in","r",stdin);
freopen("polynomial.out","w",stdout);
int n=gi(),k=gi(),len;
for (int i=0;i<n;++i) X[i]=gi();
for (len=1;len<=n;len<<=1);
inv[0]=inv[1]=1;
for (int i=2;i<len;++i) inv[i]=1ll*inv[mod%i]*(mod-mod/i)%mod;
GetSqrt(X,Y,len);memset(X,0,sizeof(X));
GetInv(Y,X,len);memset(Y,0,sizeof(Y));
Jifen(X,Y,len);memset(X,0,sizeof(X));
GetExp(Y,X,len);memset(Y,0,sizeof(Y));
GetInv(X,Y,len);memset(X,0,sizeof(X));
Y[0]=(Y[0]+1)%mod;
Getln(Y,X,len);memset(Y,0,sizeof(Y));
X[0]=(X[0]+1)%mod;
GetPow(X,Y,len,k);memset(X,0,sizeof(X));
Dao(Y,X,len);
for (int i=0;i<n-1;++i) printf("%d ",X[i]);
puts("0");return 0;
}