南昌邀请赛B题（拉格朗日插值）

题目链接：https://nanti.jisuanke.com/t/40254

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<set>
#include<ctime>
#include<vector>
#include<cmath>
#include<algorithm>
#include<map>
#define ll long long
using namespace std;
const int N=1e3+;
const int P=;
ll pre[N], suf[N], ifac[N],sum[N],a[N],fac[N];
ll Pow(ll x, int t)
{
    ll res=;
    while (t)
    {
        if (t&) res=(x*res)%P;
        x=x*x%P; t>>=;
    }
    return res;
}
void init(int n)
{
     fac[]=;
    for(int i=;i<=n+;i++)
    {
        fac[i]=fac[i-]*i%P;
    }
    for(int i=;i<=n+;i++)
    {
        ifac[i]=Pow(fac[i],P-);
    }
}
ll Lagrange(ll *y,ll n,ll k)
{
    ll ans=; pre[]=;suf[n+]=;
    for (int i=; i<=n; i++) pre[i+]=1ll*pre[i]*(k-i)%P;
    for (int i=n; i>=; i--) suf[i]=1ll*suf[i+]*(k-i)%P;

    for (int i=; i<=n; i++)
    {
        ll temp=y[i]*pre[i]%P*suf[i+]%P*ifac[i]%P*ifac[n-i]%P;
        if((n-i)&)
            ans=(ans-temp)%P;
        else
            ans=(ans+temp)%P;
    }
    return (ans%P+P)%P;
}

int main()
{
   ll T,n,m,L,R;
   cin>>T;
   init();
   while(T--)
   {
       cin>>n>>m;
       for(int i=;i<=n;i++)
       {
           cin>>a[i];
       }
       a[n+]=Lagrange(a,n,n+);
       sum[]=a[]%P;
       for(int i=;i<=n+;i++)
       {
           sum[i]=(sum[i-]+a[i])%P;
       }
       for(int j=;j<=m;j++)
       {
           cin>>L>>R;
           ll ans=Lagrange(sum,n+,R)-Lagrange(sum,n+,L-);
           cout<<(ans+P)%P<<"\n";
       }
   }
    return ;
}