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]. 
from sys import stdin


def input():
    return stdin.readline()[:-1]


def intput():
    return int(input())


def sinput():
    return input().split()


def intsput():
    return map(int, sinput())


debugging = False
def dprint(*args):
    if debugging:
        print(*args)
    else:
        pass

def ncr(n, r):
    x = 1
    for k in range(n, r, -1):
        x *= k
        x %= mod
    for k in range(n - r, 1, -1):
        x *= pow(k, mod - 2, mod)
        x %= mod
    return x

mod = 10 ** 9 + 7

# Code
n, m = intsput()
cnt = 0
for k in range(1, n + 1):
    cnt += ncr(k + m - 2, m - 1) * ncr(n - k + m, m)
    cnt %= mod
print(cnt)
