2018杭电多校第四场 1002 Harvest of Apples 莫队大法好~

Problem B. Harvest of Apples

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 1169    Accepted Submission(s): 443

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

 

莫队大法好~

先找到状态转移

用s(n,m)表示C(n,0)+C(n,1)+...+C(n,m)  那么

s(n,m)=2*s(n-1,m)-c(n-1,m);

s(n,m)=s(n,m-1)+c(n,m);

也就是说知道一个s(n,m)就能O（1）求出s(n+1,m),s(n-1,m),s(n,m+1),s(n,m-1)
 

然后瞎文明搞

注意逆元要先预处理出来

然后，就过了(当然是赛后，赛时还不会莫队，弱小可怜无助还特别能wa)

 

AC代码：

#include
#include
#include
#include
#include