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C. Two Arrays

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 $$$10^9+7$$$.

Input

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

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:

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

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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