CF575A Fibonotci

Description

Fibonotci sequence is an integer recursive sequence defined by the recurrence relation $ F_{n}=s_{n-1}·F_{n-1}+s_{n-2}·F_{n-2} $ with $ F_{0}=0,F_{1}=1 $ Sequence $ s $ is an infinite and almost cyclic sequence with a cycle of length $ N $ . A sequence $ s $ is called almost cyclic with a cycle of length $ N $ if ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF575A/489fd2e5fb549725a7a9de5a934f7a838952563f.png), for $ i>=N $ , except for a finite number of values $ s_{i} $ , for which ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF575A/3f92eca313b934333be63d48e6d251e408e4922e.png) ( $ i>=N $ ). Following is an example of an almost cyclic sequence with a cycle of length 4: s = (5,3,8,11,5,3,7,11,5,3,8,11,…) Notice that the only value of $ s $ for which the equality ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF575A/c723ac9c89791a5b8e370fa82e33937eb7ce6a73.png) does not hold is $ s_{6} $ ( $ s_{6}=7 $ and $ s_{2}=8 $ ). You are given $ s_{0},s_{1},...s_{N-1} $ and all the values of sequence $ s $ for which ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF575A/3f92eca313b934333be63d48e6d251e408e4922e.png) ( $ i>=N $ ). Find ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF575A/1ed5b2d60749876c1857042c6e156873ebb4e0f0.png).

Input Format

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Output Format

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