A12221 | Frog Jumping

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.

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.

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