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]. 
# from math import ceil
#
# T = int(input())
# ans = []
# for t in range(T):
#     n, d = (input().split(' '))
#     n, d = int(n), int(d)
#     if d <= n:
#         ans.append('YES')
#     else:
#         x = (n - 1) // 2
#         if x + ceil(d / (x + 1)) <= n and x >= 1:
#             ans.append('YES')
#         else:
#             ans.append('NO')
#     # print(n, d, ans[-1])
# for a in ans:
#     print(a)

# T = int(input())
# ans = []
# for t in range(T):
#     A, B = input().split(' ')
#     b, count = 9, 0
#     l = len(B)
#     while len(str(b)) <= l and b <= int(B):
#         b = b * 10 + 9
#         count += 1
#     ans.append(count * int(A))
# for a in ans:
#     print(a)


n, m = (map(int, input().split(' ')))
dp1 = [1] * n
for t in range(2*m - 1):
    dp2 = [0] * n
    for i in range(n):
        dp2[i] = sum(dp1[:i + 1])
    dp1 = dp2
print(sum(dp1) % (10**9 + 7))
