Harvest of Apples

Problem Description

There are n apples on a tree, numbered from 1 to n .
Count the number of ways to pick at most m apples.

 

Input

The first line of the input contains an integer T (1≤T≤105) denoting the number of test cases.
Each test case consists of one line with two integers n,m (1≤m≤n≤105) .

Output

For each test case, print an integer representing the number of ways modulo 109+7 .

 

Sample Input

2

5 2

1000 500

Sample Output

16

924129523

题解：题目要求累加组合C（n，m）m的范围（0，m）；所以如果用莫队最重要的是 弄清相邻的总和之间的关系

         并且要明白组合是如何在编程中实现的，例如C(n,m)为1到n的累乘，乘以n-m的逆元进行mod运算，乘以m的逆元再进行mod运算。

         逆元则是当前数的mod-2次方，最好在用之前就把累乘表和逆元表打好；

#include
using namespace std;
#define mod 1000000007
#define maxn 100005
#define ll long long
ll inv[maxn],fas[maxn],ans[maxn];
int pos[maxn];//记录数据所属的块
struct node
{
    int n,m,id;
}a[maxn];
bool cmp(node o,node p)
{
    return pos[o.n]==pos[p.n]?o.m>=1;
    }
    return ans;
}
void init()
{
    fas[1]=1;
    for(int i=2;i>t;
    for(int i=1;ia[i].n)
        {
            dns=(dns+C(--st,en))*inv[2]%mod;
        }
        while(ena[i].m)
        {
            dns=(dns-C(st,en--)+mod)%mod;
        }
        ans[a[i].id]=dns;
    }
    for(int i=1;i<=t;i++)//输出结果
    {
        printf("%lld\n",ans[i]);
    }
}