luogu P4781 【模板】拉格朗日插值

代码：

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
#define int long long

using namespace std;

const int N=3000,M=998244353;
int n,k,x[N],y[N],a[N*N],inv[N*N],b[N*N];

void init()
{
	scanf("%lld %lld",&n,&k);
	for (int i=1;i<=n;i++)
		scanf("%lld %lld",&x[i],&y[i]);
}

int ksm(int a,int b)
{
	int res=1;
	while(b)
	{
		if(b&1)
			res=1ll*res*a%M;
		b>>=1,a=1ll*a*a%M;
	}
	return res;
}

void work()
{
	int cnt=0;
	for (int i=1;i<=n;i++)
		for (int j=1;j<=n;j++)
		{
			if(i==j) continue;
			a[++cnt]=x[i]-x[j];
		}
//	printf("ksm:%lld",ksm(3,4));
//	printf("cnt_%lld\n",cnt);
	a[0]=1;
	for (int i=1;i<=cnt;i++)
		b[i]=a[i],a[i]=a[i-1]*a[i]%M;
	inv[cnt]=ksm(a[cnt],M-2);
	for (int i=cnt-1;i>=0;i--)
		inv[i]=1ll*inv[i+1]*b[i+1]%M;
	cnt=0;
	int ans=0;
	for (int i=1;i<=n;i++)
	{
		int tmp=y[i];
		for (int j=1;j<=n;j++)
		{
			if(i==j) continue;
			tmp=1ll*tmp*(k-x[j])%M*(inv[++cnt]*a[cnt-1]%M)%M;
		}
		ans=(ans+tmp)%M;
	}
	printf("%lld\n",(ans+M)%M);
}

signed main()
{
	init();
	work();
	return 0;
}