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]. 
n, m = input().split()
n, m = int(n),  int(m)

def twoarrays(n, m):
    
    m = 2*m 
    mod = 10**9 + 7
    dp = {}
    
    for i in range(m):
        dp[i] = {}
        
        for j in range(n):
            
            if j == 0: dp[i][j] = 1
            elif i == 0: dp[i][j] = j + 1
            else: dp[i][j] = (dp[i][j - 1] + dp[i - 1][j])%mod
            
    return dp[m - 1][n - 1]
    
print(twoarrays(n, m))