CF1288C.Two Arrays

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

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

In the first test there are $5$ suitable arrays:

• $a = [1, 1], b = [2, 2]$ ;
• $a = [1, 2], b = [2, 2]$ ;
• $a = [2, 2], b = [2, 2]$ ;
• $a = [1, 1], b = [2, 1]$ ;
• $a = [1, 1], b = [1, 1]$ .