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]. 
n, m = list(map(int,input().rstrip().split()))
from math import *

def ncr(n, r): 
  
    # p holds the value of n*(n-1)*(n-2)..., 
    # k holds the value of r*(r-1)... 
    p = 1
    k = 1
  
    # C(n, r) == C(n, n-r), 
    # choosing the smaller value 
    if (n - r < r): 
        r = n - r 
  
    if (r != 0):  
        while (r): 
            p *= n 
            k *= r 
  
            # gcd of p, k 
            m = gcd(p, k) 
  
            # dividing by gcd, to simplify product 
            # division by their gcd saves from the overflow 
            p //= m 
            k //= m 
  
            n -= 1
            r -= 1
  
        # k should be simplified to 1 
        # as C(n, r) is a natural number 
        # (denominator should be 1 )  
  
    else: 
        p = 1
  
    # if our approach is correct p = ans and k =1 
    return p

ans = 0
M= 10**9+7
for k in range(1,n+1):

    t1 = ncr(m+k-2,m-1)
    t2 = ncr(m+n-k,m)
    ans = (ans+ (t1*t2)%M)%M
    
print(ans)
    
    
