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}.
from sys import stdin
from sys import stdout
def get():
    return stdin.readline().strip()
def getf():
    return [int(i) for i in get().split()]
def put(a, end = "\n"):
    stdout.write(str(a) + end)
def putf(a):
    stdout.write(" ".join([str(i) for i in a]) + "\n")

def main():
    a, b = getf()
    ans = 0
    m = 1000000007
    ans = (b * (b - 1) // 2) * (a + b * a * (a + 1) // 2) % m
    put(ans)
main()
