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]. 
import sys

# inf = open('input.txt', 'r')
# reader = (line.rstrip() for line in inf)
reader = (line.rstrip() for line in sys.stdin)
input = reader.__next__

modulo = 10 ** 9 + 7
n, m = map(int, input().split())

# inf.close()

# D[i] - amount of non-increasing arrays ending with i
D = [1] * n
for l in range(m-1):
    leftSum = 0
    for i in range(n):
        leftSum += D[i]
        D[i] = leftSum % modulo

ans = 0
for i in range(n):
    for j in range(i, n):
        ctrA = D[i]
        ctrB = D[n-1-j]
        ans += (ctrA * ctrB) % modulo
        ans %= modulo
print(ans)
