13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T62d,

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 $$$10^9+7$$$.

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 $$$10^9+7$$$.

Note

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

$$$a = [1, 1

Two Arrays

Examples