Harvest of Apples（分块思想）

Problem B. Harvest of Apples

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 2177    Accepted Submission(s): 847

 

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

 

 

Source

2018 Multi-University Training Contest 4

 

 

Recommend

chendu   |   We have carefully selected several similar problems for you:  6343 6342 6341 6340 6339 

分析：将n分成block块预处理一下。由杨辉三角推得以下公式。

下面就是针对以上式子进行分块了。

1、先说一下分块思想。首先，如果不分块预处理的话那么可以暴力1~n，逐个求和。分块就是不爆力1~n，我们每隔block（block一般为根号下n）就暴力求一次求和。对于当前n我们找一个离着n最近的已经被分块暴力出的答案，由这个答案向n转移。这样复杂度就降低了。当然对于小于block的n直接暴力求就可以了。

2、用数组sum[i][j]代表C（n，j）的前缀和。i是从block开始加每次增加block。

3、用d数组预处暴力求得n

4、分情况讨论，n

#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
#include