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 = 1000000007

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

cur = [1 for i in range(m+n)] # cur[i] will eventually hold C(i,m)

for i in range(1,m):
    prev = cur[i-1]
    cur[i-1] = 0
    for j in range(i,m+n):
        prev, cur[j] = cur[j], prev + cur[j-1]

prev = [cur[i] for i in range(m+n)] # prev[i] holds C(i,m-1)
cur[m-1] = 0
for i in range(m,m+n):
    cur[i] = cur[i-1] + prev[i-1]

sum = 0
for i in range(1,n+1):
    sum += prev[m+i-2]*cur[m+n-i]

print(sum % MOD)
