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 = map(int, input().split())
dp1 = [[0 for _ in range(n)] for i in range(m)]
dp2 = [[0 for _ in range(n)] for i in range(m)]
for j in range(n):
    dp1[0][j] = 1
    dp2[0][j] = 1
for i in range(1, m):
    for j in range(n):
        for z in range(j, n):
            dp1[i][j] += dp1[i - 1][z]
            dp1[i][j] %= 1000000007
        for z in range(j + 1):
            dp2[i][j] += dp2[i - 1][z]
            dp2[i][j] %= 1000000007
ans = 0
for i in range(n):
    for j in range(i + 1):
        ans += dp2[-1][j] * dp1[-1][i] % 1000000007
        ans %= 1000000007
print(ans)