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 = 1100
dp = [[-1 for c in range(N)] for r in range(N) ]
MOD = 10**9 + 7

def ncr(n,r):
    if n < r : 
        return 0
    if n == r or r == 0 : 
        return 1
        
    if dp[n][r] != -1 :
        return dp[n][r]
    
    dp[n][r] = ncr(n-1,r) + ncr(n-1,r-1) 
    if dp[n][r] >= MOD :
        dp[n][r] -= MOD
    return dp[n][r]

def solve(n,m) :
    print(ncr(n=n+2*m-1,r=2*m))

while True :
    try: 
        n,d = map(int,input().split())
        solve(n,d) 

    except EOFError:
        break
