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 = map(int, input().split())
mod = 10**9 + 7

#a[m][last] - количество массивов a длиной m и с последней last
a = [[] for i in range(m+1)]
for i in range(m+1):
    a[i] = [0 for j in range(n+1)]

for i in range(1, n+1):
    a[1][i] = 1
for l in range(2, m+1):
    s = 0
    for last in range(1, n+1):
        s += a[l-1][last]
        s = s % mod
        a[l][last] = s

#b[m][last] - количество массивов b длиной m и с последней last
b = [[] for i in range(m+1)]
for i in range(m+1):
    b[i] = [0 for j in range(n+1)]

for i in range(1, n+1):
    b[1][i] = 1
for l in range(2, m+1):
    s = 0
    for last in range(n, 0, -1):
        s += b[l-1][last]
        s = s % mod
        b[l][last] = s
s = 0
for i in range(1, n+1):
    s += b[m][i]
    s = s % mod

ans = 0
for i in range(1, n+1):
    ans += a[m][i] * s
    ans %= mod
    s -= b[m][i]
    s %= mod

print(ans)

    
