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 and , where $*k*$ is some integer number in range $[1, *a*]$.

By we denote the quotient of integer division of $*x*$ and $*y*$. By 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 $1 000 000 007$ ($10^{9} + 7$). Can you compute it faster than Dreamoon?

Input

The single line of the input contains two integers $*a*$, $*b*$ ($1 ≤ *a*, *b* ≤ 10^{7}$).

Output

Print a single integer representing the answer modulo $1 000 000 007$ ($10^{9} + 7$).

Note

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

For the second sample, the set of nice integers is ${3, 5}$.