A13250 | Two Arrays
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内存限制256MB
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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 $10^9+7$ .
- 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 #1
2 2
输出 #1
5
输入 #2
10 1
输出 #2
55
输入 #3
723 9
输出 #3
157557417
In the first test there are $5$ suitable arrays:
- $a = [1, 1], b = [2, 2]$ ;
- $a = [1, 2], b = [2, 2]$ ;
- $a = [2, 2], b = [2, 2]$ ;
- $a = [1, 1], b = [2, 1]$ ;
- $a = [1, 1], b = [1, 1]$ .
- $a = [1, 1], b = [2, 2]$ ;
- $a = [1, 2], b = [2, 2]$ ;
- $a = [2, 2], b = [2, 2]$ ;
- $a = [1, 1], b = [2, 1]$ ;
- $a = [1, 1], b = [1, 1]$ .
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