hdu 5793 A Boring Question（2016第六场多校）

A Boring Question

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 487    Accepted Submission(s): 271

Problem Description

There are an equation.
∑0≤k1,k2,⋯km≤n∏1⩽j<m(kj+1kj)%1000000007=? 
We define that (kj+1kj)=kj+1!kj!(kj+1−kj)! . And (kj+1kj)=0 while kj+1<kj .
You have to get the answer for each n and m that given to you.
For example,if n=1 ,m=3 ,
When k1=0,k2=0,k3=0,(k2k1)(k3k2)=1 ;
Whenk1=0,k2=1,k3=0,(k2k1)(k3k2)=0 ;
Whenk1=1,k2=0,k3=0,(k2k1)(k3k2)=0 ;
Whenk1=1,k2=1,k3=0,(k2k1)(k3k2)=0 ;
Whenk1=0,k2=0,k3=1,(k2k1)(k3k2)=1 ;
Whenk1=0,k2=1,k3=1,(k2k1)(k3k2)=1 ;
Whenk1=1,k2=0,k3=1,(k2k1)(k3k2)=0 ;
Whenk1=1,k2=1,k3=1,(k2k1)(k3k2)=1 .
So the answer is 4.

 

 

Input

The first line of the input contains the only integer T ,(1≤T≤10000) 
Then T lines follow,the i-th line contains two integers n ,m ,(0≤n≤109,2≤m≤109) 

 

 

Output

For each n and m ,output the answer in a single line.

 

 

Sample Input

2

1 2

2 3

 

 

Sample Output

3

13

 

 

Author

UESTC

 

题意：根据题目中规定的结算方式，给定n,m的值，求结果。

 

打表找规律，比赛的时候找到了还是没写出来。。因为有除法还有取模，所以要用到逆元，第一次使用逆元，找了一个模板。

 

附上代码：

 

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#define ll long long
#define mod 1000000007
using namespace std;


ll mat(ll a,ll b)///a^b，结果对mod取膜，b的值很大的时候
{
    ll c=1;
    if(b==1) return a%mod; ///当b为1时，只剩下最后一个a
    else if(b&1)  ///b为奇数
        return mat(a,b-1)*a%mod; ///把单独的a拿出来
    else ///b为偶数
        return mat(a*a%mod,b/2)%mod; ///直接相乘，系数除以2
}

ll extend_gcd(ll a,ll b,ll &x,ll &y)
{
    if(a==0&&b==0) return -1;//无最大公约数
    if(b==0){x=1;y=0;return a;}
    ll d=extend_gcd(b,a%b,y,x);
    y-=a/b*x;
    return d;
}
//*********求逆元素*******************
//ax = 1(mod n)
ll mod_reverse(ll a,ll n)
{
    ll x,y;
    ll d=extend_gcd(a,n,x,y);
    if(d==1) return (x%n+n)%n;
    else return -1;
}

ll c(ll n,ll m)
{
    ll i,j,t1,t2,ans;
    t1=((mat(m,n+1)-1)%mod+mod)%mod;
    t2=(m-1)%mod;
    return  t1*mod_reverse(t2,mod)%mod;
}


int main()
{
    int T,n,m;
    scanf("%d",&T);
    while(T--)
    {
        scanf("%d%d",&n,&m);
        ll ans=c(n,m);
        printf("%I64d\n",ans);
    }
    return 0;
}