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())
mod = 10**9+7

DP = [0]*(n+1)
DP[0] = 1
for i in range(m):
    nxt = [0]*(n+1)
    cnt = DP[0]
    for i in range(1, n+1):
        cnt += DP[i]
        cnt %= mod
        nxt[i] = cnt
    DP = nxt

cnt = 0
ans = 0
for i in reversed(range(1,n+1)):
    cnt += DP[n-i+1]
    ans += DP[i]*cnt
    ans %= mod
print(ans)
