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 = 10**9 + 7
n,m = list(map(int,input().split()))

arr = [ [ 0 for j in range(n)] for i in range(m)]
brr = [ [ 0 for j in range(n)] for i in range(m)]
#print(arr)
#print(brr)
for i in range(m):
    for j in range(n):
        if(i != 0):
            for k in range(j,-1,-1):
                arr[i][j] += arr[i-1][k]
                arr[i][j] = arr[i][j]%mod
                

        else:
            arr[i][j] = 1

for i in range(m):
    for j in range(n):
        if(i != 0):
            for k in range(j,n):
                brr[i][j] += brr[i-1][k]
                brr[i][j] = brr[i][j]%mod

        else:
            brr[i][j] = 1

answer = 0

for i in range(n):
    for j in range(i,n):
        answer += ((arr[m-1][i]%mod)*(brr[m-1][j]%mod))%mod
        answer = answer%mod

print(answer)

