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]. 
from sys import stdin, stdout

# dp[i][j]: i col, max j
# dp[i][j] = dp[i-1][j] + dp[i][j-1]
#   1 2 3 4 5 ... n
# 1 1 2 3 4 5 ... 6
# 2 1 3
# 3
# 4
#
#  dp[1][2] => {1,2}
#  dp[2][1] => {11}
#  dp[2][2] => {12,22}, {11}
#
#
#  dp2[1][n-1] => {n, n-1}
#  dp2[2][n] => {nn}
#  dp2[2][n-1] => {nn-1,n-1n-1}, {nn}

def getsatisfyingnumbers(n,m):

    MOD = 1000000007

    # no less than
    dp = [[0 for j in range(n+1)] for i in range(m+1)]
    for i in range(1, m+1):
        dp[i][1] = 1
        for j in range(2, n+1):
            dp[i][j] = (dp[i-1][j] + dp[i][j-1]) % MOD

    #print(dp)

    # no more than
    dp2 = [[0 for j in range(n + 1)] for i in range(m + 1)]
    for i in range(1, m+1):
        dp2[i][n] = 1
        for j in range(n-1, 0, -1):
            dp2[i][j] = (dp2[i-1][j] + dp2[i][j+1]) % MOD

    #print(dp2)

    res = 0
    for i in range(1, n+1):
        for j in range(i, n+1):
            # a last digit is i, b last digit is j
            res += (dp[m][i]*dp2[m][j]) % MOD
            res = res % MOD

    return res


if __name__ == '__main__':
    nm = list(map(int, stdin.readline().split()))

    n = nm[0]
    m = nm[1]

    res = getsatisfyingnumbers(n, m)

    stdout.write(str(res))