题目描述

Bobo has a string of length 2(n + m) which consists of characters A and B. The string also has a fascinating property: it can be decomposed into (n + m) subsequences of length 2, and among the (n + m) subsequences n of them are AB while other m of them are BA.

Given n and m, find the number of possible strings modulo $(10^9+7)$.

输入格式

The input consists of several test cases and is terminated by end-of-file.

Each test case contains two integers n and m.

• $0 \leq n, m \leq 10^3$
• There are at most 2019 test cases, and at most 20 of them has $\max\{n, m\} > 50$.

输出格式

For each test case, print an integer which denotes the result.

样例

样例输入

1 2
1000 1000
0 0

样例输出

13
436240410
1