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]. 
import sys
import bisect as b
input=sys.stdin.readline
mo=10**9+7
def cin():
    return map(int,sin().split())
def ain():            
    return list(map(int,sin().split()))
def sin():
    return input()
def inin():
    return int(input())
dp=[[-1]*1001 for i in range(21)]
##print(dp[3])
def solve(i,last,n,m):
    if(dp[i][last]!=-1):
        return dp[i][last]
    if(i==m):
        dp[i][last]=1
        return 1
    ans=0
    for j in range(last,n+1):
        val=solve(i+1,j,n,m)
        ans=(ans+val%mo)%mo
    dp[i][last]=ans
    return ans

n,m=cin()
m=m*2
print(solve(0,1,n,m))
         
        
    
    
    
            
            
            
        
        
    
    
        
        
        
    
    

    
