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 fractions import Fraction


class CodeforcesTask477ASolution:
    def __init__(self):
        self.result = ''
        self.a_b = []

    def read_input(self):
        self.a_b = [int(x) for x in input().split(" ")]

    def process_task(self):
        a = Fraction(self.a_b[0], 1)
        b = Fraction(self.a_b[1], 1)
        ff = Fraction(1_000_000_007, 1)
        B = (b * (b - 1) / 2) % ff
        A1 = (a * (a + 1) / 2) % ff
        A = (A1 * b + a) % ff
        ss = (A * B) % ff
        self.result = str(int(ss))

    def get_result(self):
        return self.result


if __name__ == "__main__":
    Solution = CodeforcesTask477ASolution()
    Solution.read_input()
    Solution.process_task()
    print(Solution.get_result())
