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]. 
MOD = 10 ** 9 + 7


n, m = map(int, input().split())
ans = 0
for i in range(1, n + 1):
    dp = [[0 for _ in range(i)] for _ in range(m - 1)]
    # print(dp)
    for j in range(m - 1):
        d = 0
        for k in range(i):
            if j == 0:
                dp[j][k] = 1
                continue
            d += dp[j - 1][k]
            dp[j][k] = d
    # print(dp)
    dp2 = [[0 for _ in range(n - i + 1)] for _ in range(m)]
    for j in range(m):
        d = 0
        for k in range(n - i + 1):
            if j == 0:
                dp2[j][k] = 1
                continue
            d += dp2[j - 1][k]
            dp2[j][k] = d
    # print(dp2)
    tmp1 = 0
    tmp2 = 0
    # if len(dp) == 0:
        # print(0)
    # if len(dp2) == 0:
        # print(0)
    if len(dp) > 0:
        tmp1 = sum(dp[-1]) % MOD
    else:
        tmp1 = 1
    if len(dp2) > 0:
        tmp2 = sum(dp2[-1]) % MOD
    else:
        tmp2 = 1
    ans += (tmp1 * tmp2) % MOD
    ans %= MOD
print(ans % MOD)