302820: CF547A. Mike and Frog
Memory Limit:256 MB
Time Limit:1 S
Judge Style:Text Compare
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Solved:0
Description
Mike and Frog
题意翻译
## 题目描述 迈克有一只青蛙和一朵花,它的青蛙叫Xaniar,花叫Abol。 开始(时间为0),它的青蛙高度为 $ h_{1}$,花高度为$ h_{2}$。每一秒,迈克都会给他们两个浇水,因此每过一秒青蛙的高度都会由当前的$ h_{1}$变为$(x_{1}\times h_{1}+ y_{1}) mod\ m$,同理,花的高度都会由当前的$ h_{2}$变为$(x_{2}\times h_{2}+ y_{2}) mod\ m$。 已知$x_{1},y_{1},x_{2},y_{2}$都是整数,并且$a\ mod\ b$表示$a$除以$b$所得的余数。 迈克想知道最少多久后青蛙的高度会变成$a_{1}$ 花的高度会变成$a_{2}$。请你计算出最短时间或者告诉迈克这件事根本不会发生。 ## 输入格式 第一行一个整数$m$,$(2<=m<=10^{6})$ 第二行包含两个整数 $h_{1}$ 和$a_{1}$($0<=h_{1},a_{1}<=m$ ) 第三行包含两个整数 $x_{1}$ 和$y_{1}$($0<=x_{1},y_{1}<=m$ ) 第四行包含两个整数 $h_{2}$ 和$a_{2}$($0<=h_{2},a_{2}<=m$ ) 第五行包含两个整数 $x_{2}$ 和$y_{2}$($0<=x_{2},y_{2}<=m$ ) 输入数据保证$h_{1}≠a_{1}$ 并且 $h_{2}≠a_{2}$ ## 输出格式 如果能实现,输出最短时间;否则,输出-1即可。题目描述
Mike has a frog and a flower. His frog is named Xaniar and his flower is named Abol. Initially(at time $ 0 $ ), height of Xaniar is $ h_{1} $ and height of Abol is $ h_{2} $ . Each second, Mike waters Abol and Xaniar. ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF547A/50cf6ce14c20a4816bb68e697fff159a14a20ec2.png)So, if height of Xaniar is $ h_{1} $ and height of Abol is $ h_{2} $ , after one second height of Xaniar will become ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF547A/400a01ffe03ca079242e93f2c2d5350d22cdc247.png) and height of Abol will become ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF547A/58fd7a79d975ec6a56f22d00931ac4933868b860.png) where $ x_{1},y_{1},x_{2} $ and $ y_{2} $ are some integer numbers and ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF547A/bdb98ecde46e3f352d01af41e63fb22f595cd2ae.png) denotes the remainder of $ a $ modulo $ b $ . Mike is a competitive programmer fan. He wants to know the minimum time it takes until height of Xania is $ a_{1} $ and height of Abol is $ a_{2} $ . Mike has asked you for your help. Calculate the minimum time or say it will never happen.输入输出格式
输入格式
The first line of input contains integer $ m $ ( $ 2<=m<=10^{6} $ ). The second line of input contains integers $ h_{1} $ and $ a_{1} $ ( $ 0<=h_{1},a_{1}<m $ ). The third line of input contains integers $ x_{1} $ and $ y_{1} $ ( $ 0<=x_{1},y_{1}<m $ ). The fourth line of input contains integers $ h_{2} $ and $ a_{2} $ ( $ 0<=h_{2},a_{2}<m $ ). The fifth line of input contains integers $ x_{2} $ and $ y_{2} $ ( $ 0<=x_{2},y_{2}<m $ ). It is guaranteed that $ h_{1}≠a_{1} $ and $ h_{2}≠a_{2} $ .
输出格式
Print the minimum number of seconds until Xaniar reaches height $ a_{1} $ and Abol reaches height $ a_{2} $ or print -1 otherwise.
输入输出样例
输入样例 #1
5
4 2
1 1
0 1
2 3
输出样例 #1
3
输入样例 #2
1023
1 2
1 0
1 2
1 1
输出样例 #2
-1