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]. 
import math

MOD = 10 ** 9 + 7

n, m = map(int, input().split())
# r=[[1 if i<=j else 0 for j in range(n) ] for i in range(n)]

fact = [1] *(n + m + 5 + 2)
fact[1] = 1
for i in range(2,len(fact)):
    fact[i]=i*fact[i-1]

def komb(k, n):
    res = fact[n] // fact[k] // fact[n - k]
    if type(res) is not int:
        print(k, n)
        return
    return res


def kpowt(k, n):
    return komb(k, n + k - 1)


res = 0
for ost in range(n):
    gmin = 1 if ost else m
    for g in range(gmin, m + 1):
        dmin = m if ost == n - 1 else 0
        for d in range(dmin, m + 1):
            cze = kpowt(ost - 1, m - g + 1) if ost else 1
            cze *= kpowt(n - 1 - ost - 1, m - d + 1) if ost<n-1 else 1
            cze = cze % MOD
            res += cze

print(res % MOD)
