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 defaultdict

MOD = (10 ** 9) + 7

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

d = {}
def solve(space, take):
    key = (space, take)
    if space == 0 and take > 0:
        return 0
    if space == 0:
        return 1
    if take == 0:
        return 1
    if key in d:
        return d[key]
    res = 0
    res += solve(space, take - 1) % MOD
    res += solve(space - 1, take) % MOD
    res %= MOD
    d[key] = res
    return res

assert solve(1, 1) == 1
assert solve(2, 1) == 2
assert solve(1, 2) == 1

res = 0
for i in xrange(1, n + 1):
    for j in xrange(i, n + 1):
        l = i
        r = n - j + 1
        ll = solve(l, m) - solve(l - 1, m)
        rr = solve(r, m) - solve(r - 1, m)
        #print l, r, ll, rr
        res += ll * rr % MOD
        res %= MOD
print res


