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}.
var nums = readline().split(' ');
var a = parseInt(nums[0]);
var b = parseInt(nums[1]);
var MOD = 1000000007;

var x1,y1;
if(b%2==0)
{
    x1 = Mul(b/2,b-1);
}
else
{
    x1= Mul(b,(b-1)/2);
}
if(a%2==0)
{
    y1 = Mul(a/2,a+1);
}
else
{
    y1 = Mul(a,(a+1)/2);
}
var xx = (Mul(b,y1)+a)%MOD;
print(Mul(x1,xx));


function Mul(x,y)
{
    if(x>10000)
	{
	    var t1 = x%10000;
		var t2 = (x-t1)/10000;
		var tt1 = (y*t1)%MOD;
		var tt = (t2*y)%MOD;
		tt = (tt*10000)%MOD;
		return (tt+tt1)%MOD;
	}
	else
	{
	    return (x*y)%MOD;
	}
}