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]. 
def number(save,m,n):
    if save[m-1][n-1]==0:
        k=0
        for i in range(n,0,-1):
            k+=number(save,m-1,i)
        save[m-1][n-1]=k
        return k
    else:
        return save[m-1][n-1]
n,m=input().split()
n,m=int(n),int(m)
save=[[0 for column in range(n)] for row in range(m-1)]
save.insert(0,[i for i in range(1,n+1)])
for i in range(1,m):
    save[i][0]=1
number(save,m,n)
k,count=0,0
for i in range(n,0,-1):
    if m==1:
        count+=(i)%(10**9+7)
    else:
        k+=save[m-2][n-i]
        count+=((save[m-2][i-1]*k)%(10**9+7))
print(count%(10**9+7))