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]. 
n,m=list(map(lambda x:int(x),input().split()))


def ncr(n, r, p):
    # initialize numerator
    # and denominator
    num = den = 1
    for i in range(r):
        num = (num * (n - i)) % p
        den = (den * (i + 1)) % p
    return (num * pow(den,
            p - 2, p)) % p

mod=1000000007

temp=ncr(n+m-2,m-1,mod)

total=temp
a=n+m-2
b=m-1
maximun=n
a_1=m
b_1=m
temp_2=1
for i in range(1,n):

    num=a-b
    den=a


    temp=(((temp*num)%mod)*pow(den,mod-2,mod)%mod)%mod

    a_1+=1
    a-=1

    num=a_1
    den=a_1-m

    temp_2=((temp_2*num)%mod*pow(den,mod-2,mod)%mod)%mod

    total=(total+temp*temp_2%mod)%mod

    maximun-=1
print(total)