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]. 
from sys import stdin
input=stdin.readline
fact=[1]
    
mod= (10**9)+7
revm=[1]
def modInverse(a, m) : 
    m0 = m 
    y = 0
    x = 1
  
    if (m == 1) : 
        return 0
  
    while (a > 1) : 
  
        # q is quotient 
        q = a // m 
  
        t = m 
        m = a % m 
        a = t 
        t = y 
        y = x - q * y 
        x = t 
  
 
    if (x < 0) : 
        x = x + m0 
  
    return x 
  
for i in range(1,1001):
    fact.append(((fact[-1]%mod)*i)%mod)
    revm.append(modInverse(fact[i],mod))
n,m=map(int, input().split())
a=[]
b=[]
t3=0
for i in range(min((2*m),n)):
    t1= ( (((fact[(2*m)-1])*(revm[(2*m)-1-i]%mod))%mod)*(revm[i]%mod) )%mod
    t2=((((fact[n])*(revm[n-i-1]%mod))%mod)*(revm[i+1])%mod)%mod
    t3=((((t1%mod)*(t2%mod))%mod)+(t3%mod))%mod
print(t3)        
    
