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]. 

def solve(n, m):
    mod = 10 ** 9 + 7
    dp = [[0] * n for i in range(2 * m)]
    for i in range(n):
        dp[0][i] = 1;
    for i in range(1, 2*m):
        sum = 0;
        for j in range(n):
            sum += dp[i-1][j];
            sum %= mod;
            dp[i][j] = sum;
    
    ans = 0;
    for j in range(len(dp[2*m-1])):
        ans += dp[2*m-1][j]
        ans %= mod
    return ans;
            

inp = input().strip().split();
A = int(inp[0])
B = int(inp[1])
print(solve(A, B));
    
    
    