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
mod=10**9+7
def power(x,y,m):
    if y==0:
        return 1
    p=power(x,y//2,m)
    p=(p*p)%m
    if (y&1):
        p=(p*x)%m
    return p
def modinverse(a,m):
    return power(a,m-2,m)
fact=[1]
for i in range(1,1500):
    fact.append((i*fact[-1])%mod)
#print(fact)
n,m=map(int,sys.stdin.readline().split())
a,b=modinverse(fact[2*m],mod),modinverse(fact[n-1],mod)
#print(a,b)
print((fact[n+2*m-1]*modinverse(fact[2*m],mod)*modinverse(fact[n-1],mod))%mod)
