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}.
MOD = 10**9 + 7

def msum(n):
    return ((n * (n + 1)) // 2) % MOD

def main1():
    A, B = list(map(int, input().split()))
    S = 0

    for i in range(1,B):
        lo = i
        hi = (A + 1) * i - 1
        t = (msum(hi) - msum(lo - 1)) % MOD
        while t < 0:
            t += MOD
        cur = (i * (hi - lo + 1) + B * t) % MOD
        while cur < 0:
            cur += MOD

        S = (S + cur) % MOD

    print(S)

def main2():
    A, B = list(map(int, input().split()))
    sol = (B - 1) * B * A *(2 + B * (A + 1)) // 4
    print(sol % MOD)

main2()
