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 operator as op
from functools import reduce

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

MOD = 1000000007
def ncr(cn, r):
    if( r > cn ):
        return 0
    r = min(r, cn-r)
    numer = reduce(op.mul, range(cn, cn-r, -1), 1)
    denom = reduce(op.mul, range(1, r+1), 1)
    return numer // denom


ans = 0
for i in range( 1, min(2*m+1, n+1) ):
    a1 = ncr( n, i )
    a2 = ncr( 2*m-1, i-1 )
    ans = (ans+(a1*a2)%MOD)%MOD
print(int(ans%MOD))