Two Arrays

题意翻译

输入两整数 $n$、$m$，求有多少对正整数序列 $a_i$、$b_i$ 满足： * $a_i$、$b_i$ 的长度为 $m$； * $a_i$、$b_i$ 中所有元素的值小于等于 $n$； * 对于所有 $1\le i\le m$，$a_i\le b_i$； * 序列 $a$ 单调不降，序列 $b$ 单调不升。 答案对 $10^9+7$ 取模。

题目描述

You are given two integers $ n $ and $ m $ . Calculate the number of pairs of arrays $ (a, b) $ such that: - the length of both arrays is equal to $ m $ ; - each element of each array is an integer between $ 1 $ and $ n $ (inclusive); - $ a_i \le b_i $ for any index $ i $ from $ 1 $ to $ m $ ; - array $ a $ is sorted in non-descending order; - array $ b $ is sorted in non-ascending order. As the result can be very large, you should print it modulo $ 10^9+7 $ .

输入输出格式

输入格式

The only line contains two integers $ n $ and $ m $ ( $ 1 \le n \le 1000 $ , $ 1 \le m \le 10 $ ).

输出格式

Print one integer – the number of arrays $ a $ and $ b $ satisfying the conditions described above modulo $ 10^9+7 $ .

输入输出样例

输入样例 #1

2 2

输出样例 #1

5

输入样例 #2

10 1

输出样例 #2

55

输入样例 #3

723 9

输出样例 #3

157557417

说明

In the first test there are $ 5 $ suitable arrays: - $ a = [1, 1], b = [2, 2] $ ; - $ a = [1, 2], b = [2, 2] $ ; - $ a = [2, 2], b = [2, 2] $ ; - $ a = [1, 1], b = [2, 1] $ ; - $ a = [1, 1], b = [1, 1] $ .