Frog Jumping

2000ms

524288K

Description:

A frog is currently at the point $$$0$$$ on a coordinate axis $$$Ox$$$. It jumps by the following algorithm: the first jump is $$$a$$$ units to the right, the second jump is $$$b$$$ units to the left, the third jump is $$$a$$$ units to the right, the fourth jump is $$$b$$$ units to the left, and so on.

Formally:

if the frog has jumped an even number of times (before the current jump), it jumps from its current position $$$x$$$ to position $$$x+a$$$;
otherwise it jumps from its current position $$$x$$$ to position $$$x-b$$$.

Your task is to calculate the position of the frog after $$$k$$$ jumps.

But... One more thing. You are watching $$$t$$$ different frogs so you have to answer $$$t$$$ independent queries.

Input:

The first line of the input contains one integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of queries.

Each of the next $$$t$$$ lines contain queries (one query per line).

The query is described as three space-separated integers $$$a, b, k$$$ ($$$1 \le a, b, k \le 10^9$$$) — the lengths of two types of jumps and the number of jumps, respectively.

Output:

Print $$$t$$$ integers. The $$$i$$$-th integer should be the answer for the $$$i$$$-th query.

Sample Input:

6
5 2 3
100 1 4
1 10 5
1000000000 1 6
1 1 1000000000
1 1 999999999

Sample Output:

Note:

In the first query frog jumps $$$5$$$ to the right, $$$2$$$ to the left and $$$5$$$ to the right so the answer is $$$5 - 2 + 5 = 8$$$.

In the second query frog jumps $$$100$$$ to the right, $$$1$$$ to the left, $$$100$$$ to the right and $$$1$$$ to the left so the answer is $$$100 - 1 + 100 - 1 = 198$$$.

In the third query the answer is $$$1 - 10 + 1 - 10 + 1 = -17$$$.

In the fourth query the answer is $$$10^9 - 1 + 10^9 - 1 + 10^9 - 1 = 2999999997$$$.

In the fifth query all frog's jumps are neutralized by each other so the answer is $$$0$$$.

The sixth query is the same as the fifth but without the last jump so the answer is $$$1$$$.

Informação

Provedor Codeforces

Código CF1532B