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=map(int,input().split())

pre=[]

ss=[0]*(n+1)
s=[0]+[1]*(n)

pre.append(ss)
pre.append(s)

for i in range(2,m+1):
    h=[0]
    for j in range(1,n+1):
        h.append((pre[i-1][j]+h[-1])%MOD)

    pre.append(h)

#print(pre)

arr=pre[m]

dp=[arr[0]]
for i in range(1,len(arr)):
    dp.append((dp[-1]+arr[i])%MOD)


ans=0
ptr=len(dp)-1

for i in range(1,len(arr)):

    ans=(ans+((arr[i]*dp[ptr])%MOD))%MOD
    ptr=(ptr-1)%MOD

print(ans%MOD)
        
