Sigma (化简）牛客多校第一场 -- Integration

思路：

可以裂项化简，类似找规律，可以两项、三项代进去试试看。

#define IOS ios_base::sync_with_stdio(0); cin.tie(0);
#include <cstdio>//sprintf islower isupper
#include <cstdlib>//malloc  exit strcat itoa system("cls")
#include <iostream>//pair
#include <fstream>
#include <bitset>
//#include <map>
//#include<unordered_map>
#include <vector>
#include <stack>
#include <set>
#include <string.h>//strstr substr
#include <string>
#include <time.h>//srand(((unsigned)time(NULL))); Seed n=rand()%10 - 0~9;
#include <cmath>
#include <deque>
#include <queue>//priority_queue<long long, vector<long long>, greater<long long> > q;//less
#include <vector>//emplace_back
//#include <math.h>
//#include <windows.h>//reverse(a,a+len);// ~ ! ~ ! floor
#include <algorithm>//sort + unique : sz=unique(b+1,b+n+1)-(b+1);+nth_element(first, nth, last, compare)
using namespace std;//next_permutation(a+1,a+1+n);//prev_permutation
#define mem(a,b) memset(a,b,sizeof(a))
#define fo(a,b,c) for(a=b;a<=c;++a)//register long long i
#define fr(a,b,c) for(a=b;a>=c;--a)
#define pr printf
#define sc scanf
void swapp(long long &a,long long &b);
double fabss(double a);
long long maxx(long long a,long long b);
long long minn(long long a,long long b);
long long Del_bit_1(long long n);
long long lowbit(long long n);
long long abss(long long a);
//const long long INF=(1LL<<60);
const double E=2.718281828;
const double PI=acos(-1.0);
const long long inf=(1<<29);
const double ESP=1e-9;
const long long mod=(long long)1e9+7;
const long long N=(long long)1e6+6;

long long a[N];
long long qpow(long long a,long long b,long long mod)
{
    long long ans;
    a%=mod;
    ans=1;
    while(b!=0)
    {
        if(b&1)
            ans=(ans*a)%mod;
        b/=2;
        a=(a*a)%mod;
    }
    return ans;
}

int main()
{
    long long n,i;
    while(~sc("%lld",&n))
    {
        for(i=1;i<=n;++i)
            sc("%lld",&a[i]);
        long long ans=0;
        for(i=1;i<=n;++i)
        {
            long long temp=a[i]*2;
            for(long long j=1;j<=n;++j)
            {
                if(j==i)
                    continue;
                temp*=((a[j]*a[j]-a[i]*a[i])%mod+mod)%mod;
                temp%=mod;
            }
            ans+=qpow(temp,mod-2,mod);
            ans%=mod;
        }
        pr("%lld
",ans);
    }
    return 0;
}

/**************************************************************************************/

long long maxx(long long a,long long b)
{
    return a>b?a:b;
}

void swapp(long long &a,long long &b)
{
    a^=b^=a^=b;
}

long long lowbit(long long n)
{
    return n&(-n);
}

long long Del_bit_1(long long n)
{
    return n&(n-1);
}

long long abss(long long a)
{
    return a>0?a:-a;
}

double fabss(double a)
{
    return a>0?a:-a;
}

long long minn(long long a,long long b)
{
    return a<b?a:b;
}