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, sz = map(int, input().split())
 
waysA = [[0 for _ in range(n + 1)] for _ in range(sz + 1)]
waysB = [[0 for _ in range(n + 1)] for _ in range(sz + 1)]
for size in range(1, sz + 1):
    for cur in range(1, n + 1):
        if size == 1:
            waysA[size][cur] = 1
            waysB[size][cur] = 1
            continue
        for prev in range(1, cur + 1):
            waysA[size][cur] += waysA[size - 1][prev]
            waysA[size][cur] %= MOD
        for prev in range(cur, n + 1):
            waysB[size][cur] += waysB[size - 1][prev]
            waysB[size][cur] %= MOD

ret = 0
for a in range(1, n + 1):
    for b in range(a, n + 1):
        ret += (waysA[sz][a] * waysB[sz][b])
        ret %= MOD
print(ret)