Dreamoon loves summing up something for no reason. One day he obtains two integers a and b occasionally. He wants to calculate the sum of all nice integers. Positive integer x is called nice if <image> and <image>, where k is some integer number in range [1, a].

By <image> we denote the quotient of integer division of x and y. By <image> we denote the remainder of integer division of x and y. You can read more about these operations here: http://goo.gl/AcsXhT.

The answer may be large, so please print its remainder modulo 1 000 000 007 (109 + 7). Can you compute it faster than Dreamoon?

Input

The single line of the input contains two integers a, b (1 ≤ a, b ≤ 107).

Output

Print a single integer representing the answer modulo 1 000 000 007 (109 + 7).

Examples

Input

1 1


Output

0


Input

2 2


Output

8

Note

For the first sample, there are no nice integers because <image> is always zero.

For the second sample, the set of nice integers is {3, 5}.
inf=list(map(int,input().split()))
a=inf[0]
b=inf[1]
ans=0
p=int(a*(a+1)/2)
nn=b-1
q=int(nn*(nn+1)/2)
ans=(p*b+a)*q
"""for i in range(1,b):
    k=p*i*b+i*a
    ans+=k"""

ans=ans%(10**9+7)
print(ans)
     											    	 	  	   	