# Two arrays

Easy

Execution time limit is 1 second

Runtime memory usage limit is 128 megabytes

You are given two numbers $n$ and $m$. Find the number of pairs of arrays $(a,b)$ such that:

both arrays have a length of $m$;

each element of both arrays is an integer from $1$ to $n$ inclusive;

$a_{i}≤b_{i}$ for every index $i$ from $1$ to $m$;

array $a$ is sorted in non-decreasing order;

array $b$ is sorted in non-increasing order.

Since the result may be too large, compute it modulo $10_{9}+7$.

## Input

Two positive integers $n$ and $m(1≤n≤1000,1≤m≤10)$.

## Output

Print a single number — the number of arrays $a$ and $b$ that satisfy the conditions described above. Print the result modulo $10_{9}+7$.

## Examples

Input #1

Answer #1

Input #2

Answer #2

Submissions 25

Acceptance rate 12%