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]. 

def modmal(a,b,mod):

    return a * b % mod




def moddiv(a,b,mod):

    return (a * pow(b,mod-2)) % mod

def inverse(a,mod):
    return pow(a,mod-2)

def modfac(n, MOD):
 
    f = 1
    factorials = [1]
    for m in range(1, n + 1):
        f *= m
        f %= MOD
        factorials.append(f)
    inv = pow(f, MOD - 2, MOD)
    invs = [1] * (n + 1)
    invs[n] = inv
    for m in range(n, 1, -1):
        inv *= m
        inv %= MOD
        invs[m - 1] = inv
    return factorials, invs


def modnCr(n,r,mod,fac,inv):

    return fac[n] * inv[n-r] * inv[r] % mod


for loop in range(1):

        

        n,m = map(int,input().split())
        mod = 10 ** 9 + 7
        ans = 0
        fac,inv = modfac(1010,mod)

        for i in range(n):
            i += 1

            for j in range(i):

                j += 1

                ans += modnCr(m+j-2,j-1,mod,fac,inv) * modnCr(m+n-i-1,n-i,mod,fac,inv)
                ans %= mod

        print (ans)
