CF1077A.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.

一只青蛙当前位于坐标轴 $Ox$ 上的点 $0$ 处。它按照以下规则跳跃：第一次向右跳 $a$ 个单位，第二次向左跳 $b$ 个单位，第三次向右跳 $a$ 个单位，第四次向左跳 $b$ 个单位，依此类推。

形式化地定义如下：

• 若青蛙在当前跳跃之前已跳跃偶数次，则它从当前位置 $x$ 跳至位置 $x+a$；
• 否则，它从当前位置 $x$ 跳至位置 $x-b$。

你的任务是计算青蛙经过 $k$ 次跳跃后的位置。

但是……还有一点：你正在同时观察 $t$ 只不同的青蛙，因此你需要回答 $t$ 个相互独立的查询。

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.

输入的第一行包含一个整数 $t$（$1 \le t \le 1000$），表示查询次数。

接下来的 $t$ 行每行包含一个查询（每行一个查询）。

每个查询由三个以空格分隔的整数 $a, b, k$（$1 \le a, b, k \le 10^9$）描述，分别表示两种跳跃的长度以及跳跃总次数。

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

输出 $t$ 个整数。其中第 $i$ 个整数应为第 $i$ 个查询的答案。

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 $1$.

第一次查询中，青蛙向右跳 $5$，向左跳 $2$，再向右跳 $5$，因此答案为 $5 - 2 + 5 = 8$。

第二次查询中，青蛙向右跳 $100$，向左跳 $1$，向右跳 $100$，再向左跳 $1$，因此答案为 $100 - 1 + 100 - 1 = 198$。

第三次查询中，答案为 $1 - 10 + 1 - 10 + 1 = -17$。

第四次查询中，答案为 $10^9 - 1 + 10^9 - 1 + 10^9 - 1 = 2999999997$。

第五次查询中，青蛙的所有跳跃相互抵消，因此答案为 $0$。

第六次查询与第五次相同，但缺少最后一次跳跃，因此答案为 $1$。