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=list(map(int,input().split()))
matrix=[[0]*n for i in range(m)]
prefixSum=[[0]*n for i in range(m)]
z=(10**9)+7
for i in range(m):
    matrix[i][0]=1
    prefixSum[i][0]=1
for i in range(1,n):
    matrix[0][i]=(((i+1)*(i+2))//2)%z
    prefixSum[0][i]=(prefixSum[0][i-1]+matrix[0][i])%z
for i in range(1,m):
    for j in range(1,n):
        matrix[i][j]=(matrix[i][j-1]+prefixSum[i-1][j])%z
        prefixSum[i][j]=(prefixSum[i][j-1]+matrix[i][j])%z
print(matrix[m-1][n-1])
