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
MAX=1019
fact=[1]
for zz in range(1,MAX+1):
    fact.append(((fact[-1]%MOD)*zz%MOD)%MOD) #with MOD
#    fact.append(fact[-1]*zz) #without MOD
def nCr(n,r): #choose, MOD is prime
    num=fact[n]
    den=((fact[r]%MOD)*(fact[n-r]%MOD))%MOD #with MOD
    return ((num%MOD)*pow(den,MOD-2,MOD))%MOD #with MOD
#    den= fact[r]*fact[n-r]# without MOD
#    return num//den # without MOD

n,m=[int(x) for x in input().split()]

#a and b[::-1] put together is just a sorted array containing numbers from 1 to n
#choose 2m elements from n elements with repetition

ans=nCr(n+2*m-1,2*m)

print(ans)