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=input().split()
n=int(n)
m=int(m)
mod=1000000000+7
l=[[0 for i in range(0,1001)]for j in range(0,11)]
for i in range(1,1001):
    l[0][i]=1 
for i in range(1,11):
    for j in range(1,1001):
        l[i][j]=(l[i-1][j]%mod+l[i][j-1]%mod)%mod
b=list()
a=list()
for i in range(0,n+1):
    b.append(0)
    a.append(0)
for i in range(1,n+1):
    a[i]=l[m-1][i]
for i in range(1,n+1):
    b[i]=l[m][n+1-i]
for i in range(1,n+1):
    b[i]=(b[i]*a[i])%mod
sum1=0
for i in range(1,n+1):
    sum1=(sum1+b[i])%mod
print(sum1)  