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 math import *

mod=1000000007
tmp=0

f=[]
fact=1
f.append(fact)

for i in range(1,2000):
    fact=(fact*i)%mod
    f.append(fact)

def power(x,y):
    res=1
    while y:
        if y%2:
            res=(res*x)%mod

        y=y//2
        x=(x*x)%mod

    return res

def ncr(n,r):
	tmp=(power(f[r],mod-2)*f[n])%mod
	tmp=(tmp*power(f[n-r],mod-2))%mod

	return tmp


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

a=[]
a1=0
b=0
ans=0

for j in range(1,n+1):
	a1=(a1+ncr(j+m-2,m-1))%1000000007
	a.append(a1)

for i in range(1,n+1):
	b=ncr((n+m-i-1),m-1)
	# print('b', i,b)
	ans=(ans+(b*a[i-1]))%1000000007

print(ans)