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 ≤ 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.

Input

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

Output

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

Examples

Input

2 2

Output

5

Input

10 1

Output

55

Input

723 9

Output

157557417

Note

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].

inputFormat

Input

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

outputFormat

Output

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

Examples

Input

2 2

Output

5

Input

10 1

Output

55

Input

723 9

Output

157557417

Note

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].

样例

723 9

157557417

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