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]. 
# coding=utf-8
# Date: 2020-01-08
# Author: lee215

get = lambda: int(raw_input().strip())
getl = lambda: raw_input().strip()
gets = lambda: map(int, raw_input().strip().split())
getss = lambda n: [gets() for _ in xrange(n)]


# fi = open('sample3.in', 'r')
# raw_input = fi.readline


mod = 10**9 + 7


def inv(x):
    return pow(x, mod - 2, mod)


def C2(a, b):
    return dp[a + m - 2]

n, m = gets()


dp = [1] * (n + m)
for i in xrange(m, n + m):
    dp[i] = dp[i - 1] * i % mod * inv(i - m + 1) % mod


res = 0
for i in xrange(1, n + 1):
    for j in xrange(i, n + 1):
        res += C2(i, m - 1) * C2(n - j + 1, m - 1) % mod
        res %= mod
print res
