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]. 
pri=10**9+7
fact=[0 for i in range(10**4+1)]
fact[0]=1
fact[1]=1

for i in range(2,len(fact)):
    fact[i]=(i*(fact[i-1]%pri))%pri
    
ifact=[0 for i in range(10**4+1)]
ifact[1]=1
ifact[0]=1
def mod(a,y,pri):
    if(y==0):
        return 1;
    else:
        p=mod(a,y//2,pri)%pri
        p=(p*p)%pri
        if(y%2==0):
            return p;
        else:
            return (a*p)%pri;
        
for i in range(2,10**4+1):
    ifact[i]=(ifact[i-1]*mod(i,pri-2,pri))%pri
    
def NcR(n,r):
    ret=(ifact[n-r]*ifact[r])%pri
    ret=(ret*fact[n])%pri
    return ret;
n,m=map(int,input().split())
print(NcR(n+2*m-1,n-1))    
