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]. 
import io
import os

from collections import Counter, defaultdict, deque


def solve(N, M):
    MOD = 10 ** 9 + 7

    # Num non-desc subseq of length M ending in i
    ways = [1 for i in range(N)]
    for i in range(M - 1):
        nextWays = [0 for i in range(N)]
        for j in range(N):
            if j:
                nextWays[j] += nextWays[j - 1]
            nextWays[j] += ways[j]
            nextWays[j] %= MOD
        ways = nextWays
    ans = 0
    for i in range(N):
        for j in range(i, N):
            ans += ways[i] * ways[N - j - 1]
            ans %= MOD
    return ans % MOD


if __name__ == "__main__":
    input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

    N, M = [int(x) for x in input().split()]
    ans = solve(N, M)
    print(ans)
