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 sys
from collections import deque


buff = []
cur = 0


def ni():
    global buff, cur
    if cur < len(buff):
        cur = cur + 1
        return buff[cur - 1]
    cur = 0
    data = sys.stdin.readline().split(' ')
    buff = [int(g) for g in data]
    return ni()

MOD = 1000000007

def pow(x, m):
    if m == 0:
        return 1
    if m == 1:
        return x
    a = pow(x, m / 2)
    a = a * a % MOD
    if m % 2 == 1:
        a = a * x
    return a % MOD

def inv(x):
    return pow(x, MOD - 2)

fact = [1]
ifact = [1]
for i in range(1, 1020):
    fact.append(fact[-1] * i % MOD)
    ifact.append(ifact[-1] * inv(i) % MOD)


def c(n, k):
    return (fact[n] * ifact[k] % MOD) * ifact[n - k] % MOD

def ct_array(len, max):
    return c(len + max - 1, max - 1)


n = ni()
m = ni()


ans = 0
for fe in range(1, n + 1):
    for se in range(fe, n + 1):
        # print ct_array(m - 1, fe),  ct_array(m - 1, n - se + 1)
        ans = ans + ct_array(m - 1, fe) * ct_array(m - 1, n - se + 1) % MOD


print ans % MOD