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]. 
fac = [1 for _ in range(1021)]
ifac = [1 for _ in range(1021)]
mod = 10**9+7

def ModInv(x, y) :
    res = 1;
    while (y > 0):
        if (y & 1):
            res = (res*x) % mod;
        y = y>>1;
        x = (x*x) % mod;
    return res;

for i in range(1, 1020):
    fac[i] = (fac[i-1]*i)%mod
    ifac[i] = (ifac[i-1]*ModInv(i, mod-2))%mod

for _ in range(1):
    n, m = map(int, input().split())
    ans = (fac[n+2*m-1]*(ifac[2*m]*ifac[n-1])%mod)%mod
    print(ans)