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]. 
#!/usr/bin/env python

from collections import deque, defaultdict
import itertools as ite
import sys
import math
import decimal

sys.setrecursionlimit(1000000)

INF = 10 ** 18
MOD = 10 ** 9 + 7

DP = [[0] * 11 for i in range(1100)]
DP[1][0] = 1

for i in range(1, 11):
    S = 0
    for j in range(1, 1001):
        S += DP[j][i - 1]
        S %= MOD
        DP[j][i] = S

# print DP[:3]

n, m = map(int, raw_input().split())

memo = [0] * 1100
S = 0
for i in range(1, n + 1):
    S += DP[i][m]
    S %= MOD
    memo[i] = S
ans = 0
for i in range(1, n + 1):
    ans += DP[i][m] * memo[n - i + 1] % MOD
    ans %= MOD
print ans % MOD
