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]. 
MOD = int (1e9 + 7)

read = input ().split ()
n = int (read[0])
m = int (read[1])

f = [[0 for i in range (n + 1)] for j in range (m + 1)]

for i in range (1, n + 1) :
    f[1][i] = 1

for i in range (2, m + 1) :
    f[i][1] = 1
    for j in range (2, n + 1) :
        f[i][j] = f[i][j - 1] + f[i - 1][j]

ans = 0
for i in range (1, n + 1) :
    tmp = 0
    for j in range (1, n - i + 2) :
        tmp += f[m][j]
        tmp %= MOD
    ans += f[m][i] * tmp
    ans %= MOD

print (ans % MOD)



  	 	 	  			 			   	 	   			 		