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}.
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def main():
    MOD = int(1e9) + 7
    a , b = map(int , input().split())
    k1 = ((b - 1)*b)//2
    k2 = ((a + 1)*a)//2
    k1 %= MOD
    k2 %= MOD
    ans = (k2 * b + a)%MOD
    ans = (ans * k1)%MOD
    print(ans)
    return

if __name__ == "__main__":
    main()