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]. 


'''
  upsolving:
  ~~~~~~~~~~
  
  ->  a1..am bm..b1 
    
    no. of combinations of
    n-1 sticks and 2m boxes
      all boxes before first stick filled with 1
      .
      .
      all boxes before n-1 stick filled with n-1
      all boxes after  n-1 stick filled with n 
      
      
      number integral solutions to (s.t xi = 0 is allowed)
          x1 + x2 + .. + xn = 2*m   
   
   =>  ( 2*m + n - 1 ) C  (n  - 1 )
   
   https://codeforces.com/blog/entry/73105
   
   -> implementation of factorial simpler in python
  
   
'''

from math import factorial as fact

mod = 10**9 + 7


def Cmb(n, k):
    return fact(n) // ( fact(k) * fact(n-k) )
    
n, m = map( int, input().split() )
print(Cmb(n + 2*m - 1, n -1) % mod)

