Frog Jumping

题目详情 - 蛙跳 - ACjudge

题面翻译

题目描述

对于给定的$a,b,k$，初始状态$x=0$，第$i$次操作满足以下规则：

• $i$为奇数，$x=x+a$
• $i$为偶数，$x=x-b$

求$k$次操作后$x$的值

输入格式

题目有多组数据 第一行一个整数$t(1\leq t\leq1000)$表示数据组数 接下来$t$行，每行三个整数$a,b,k(1\leq a,b,k\leq10^9)$表示每组数据

输出格式

输出共$t$行，第$i$行表示第$i$组数据的答案

题目描述

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.

输入格式

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.

输出格式

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

样例 #1

样例输入 #1

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

样例输出 #1

8
198
-17
2999999997
0
1

提示

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 $1$ .