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C. Dreamoon and Sums

time limit per test

1.5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputDreamoon 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).

Examples

Input

1 1

Output

0

Input

2 2

Output

8

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}.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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