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
range = xrange
input = raw_input
MOD = 10**9 + 7
n, m = [int(x) for x in input().split()]

big = 1001

DP = [[0]*big for _ in range(m)]
DP[0] = [1] * big
for i in range(1, m):
    prevDP = DP[i - 1]
    dp = DP[i]

    s = 0
    for j in range(big):
        dp[j] = s = (s + prevDP[j]) % MOD
dp = DP[-1]

ways = 0
for i in range(1, n + 1):
    for j in range(i, n + 1):
        ways = (ways + dp[i - 1] * dp[n - j]) % MOD

print ways

