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 binomialCoef(n, k): 
    C = [[0 for x in range(k+1)] for x in range(n+1)] 
  
    for i in range(n+1): 
        for j in range(min(i, k)+1): 
            if j == 0 or j == i: 
                C[i][j] = 1
  
            else: 
                C[i][j] = C[i-1][j-1] + C[i-1][j] 
  
    return C[n][k] 


n,m=list(map(int,input().strip().split()))
a=10**9+7
print(binomialCoef(n+2*m-1,2*m)%a)    