题目

https://codeforces.com/gym/103119/problem/A

分析

https://fanfansann.blog.csdn.net/article/details/118528285
这篇博客讲得好清楚了。

代码

#include <bits/stdc++.h>
using namespace std;

#define MAXN 100005

#define Ha 998244353
#define GHa 3

long long A_[MAXN<<2], B_[MAXN<<2], C_[MAXN<<2];
int RR[MAXN<<2];

long long a[MAXN];

long long jc[MAXN];


long long ksm(long long x, int k)
{
	long long ret=1;
	for (; k; x=x*x%Ha,k>>=1)
		if (k&1) ret=ret*x%Ha;
	return ret;
}


void NTT(int len, long long *A, int type)
{
	for (int i=0; i<len; i++)
		if (i<RR[i])
			swap(A[i], A[RR[i]]);
	for (int mid=1; mid<len; mid<<=1) {
		long long wn=ksm(GHa, (Ha-1)/(mid<<1));
		for (int pos=0; pos<len; pos+=(mid<<1)) {
			long long w=1;
			for (int k=0; k<mid; k++, w= w*wn%Ha) {
				long long x= A[pos+k];
				long long y= w*A[pos+mid+k]%Ha;
				A[pos+k]=(x+y)%Ha;
				A[pos+k+mid]=(x-y+Ha)%Ha;
			}
		}
	}
	if (type==1)
		return;
	for (int i=(len>>1)-1; i>0; i--)
		swap(A[i], A[len-i]);
	long long inv= ksm(len, Ha-2);
	for (int i=0; i<len; i++)
		A[i]= A[i]*inv %Ha;
}



void NTT_mul(long long *A, long long *B, long long *C, int n, int m)
{
	int len=1, L=0;
	while (len<=n+m) len<<=1, L++;
	
	for (int i=n+1; i<len; i++) A[i]=0;
	for (int i=m+1; i<len; i++) B[i]=0;
	
	for (int i=0; i<len; i++)
		RR[i]= (RR[i>>1] >> 1) | ((i&1) << (L-1));
	
	NTT(len, A, 1);
	NTT(len, B, 1);
	for (int i=0; i<len; i++)
		C[i]= A[i]*B[i] %Ha;
	NTT(len, C, -1);
}




void fun(int L, int R, vector<long long> &f)
{
	
	if (L==R) {
		f[0]=1;
		f[1]=a[L];
		return;
	}
	int M=(L+R)>>1;
	int len1=M-L+1, len2=R-M;
	vector<long long> f1(len1+3),f2(len2+3);
	fun(L,M,f1);
	fun(M+1,R,f2);
	
	A_[0]=B_[0]=C_[0]=1;
	for (int i=1; i<=len1; i++) A_[i]=f1[i];
	for (int i=1; i<=len2; i++) B_[i]=f2[i];
	
	NTT_mul(A_,B_,C_,len1,len2);
	
	for (int i=R-L+1; i>0; i--)
		f[i]=C_[i];
	
	/*
	printf("[%d %d]\n  ",L,R);
	for (int i=0; i<=len1; i++)
		printf("%lld ",f1[i]);
	printf("\n  ");
	for (int i=0; i<=len2; i++)
		printf("%lld ",f2[i]);
	printf("\n  ");
	for (int i=0; i<=R-L+1; i++)
		printf("%lld ",f[i]);
	printf("\n");
	*/
}



void solve()
{
	int n;
	scanf("%d",&n);
	for (int i=1; i<=n; i++) scanf("%lld",&a[i]);
	vector<long long> f(n+1);
	fun(1, n, f);
	
	long long ans=0;
	for (int i=1; i<=n; i++) {
		ans+=f[i]*jc[i] %Ha *jc[n-i] %Ha;
		ans%=Ha;
	}
	ans*=ksm(jc[n], Ha-2);
	ans%=Ha;
	
	printf("%lld\n",ans);
}



void pre()
{
	jc[0]=1;
	for (int i=1; i<=MAXN; i++)
		jc[i]=jc[i-1]*i %Ha;
}


int main()
{
	pre();
	
	int ttt;
	scanf("%d",&ttt);
	while (ttt--) {
		solve();
	}
	
	return 0;
}