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, raw_input().split())
dp1=[[-1]*(n+1) for _ in xrange(m+1)]
dp2=[[-1]*(n+1) for _ in xrange(m+1)]
def f(m, l):
    if m==1:
        return 1
    if dp1[m][l]!=-1:
        return dp1[m][l]
    a=0
    for i in xrange(1, l+1):
        a+=f(m-1, i)
    dp1[m][l]=a
    return a        
for i in range(1, n+1):
    f(m, i)
def f2(m, l):
    if m==1:
        return 1
    if dp2[m][l]!=-1:
        return dp2[m][l]
    a=0
    for i in xrange(l, n+1):
        a+=f2(m-1, i)
    dp2[m][l]=a
    return a
for i in range(1, n+1):
    f2(m, i)
mod=10**9+7
a=0
for i in xrange(1, n+1):
    for j in xrange(i, n+1):
        a+=dp1[m][i]*dp2[m][j]

print a%mod
