Anniversary

题意翻译

设$F$是斐波那契数列，在$[l,r]$中选$k$个数$a_{1}...a_{k}$,使得$gcd(F_{a_{1}},F_{a_{2}},...,F_{a_{k}})$尽可能大。输出对$m$取模后的结果。

题目描述

There are less than 60 years left till the 900-th birthday anniversary of a famous Italian mathematician Leonardo Fibonacci. Of course, such important anniversary needs much preparations. Dima is sure that it'll be great to learn to solve the following problem by the Big Day: You're given a set $ A $ , consisting of numbers $ l $ , $ l+1 $ , $ l+2 $ , $ ... $ , $ r $ ; let's consider all its $ k $ -element subsets; for each such subset let's find the largest common divisor of Fibonacci numbers with indexes, determined by the subset elements. Among all found common divisors, Dima is interested in the largest one. Dima asked to remind you that Fibonacci numbers are elements of a numeric sequence, where $ F_{1}=1 $ , $ F_{2}=1 $ , $ F_{n}=F_{n-1}+F_{n-2} $ for $ n>=3 $ . Dima has more than half a century ahead to solve the given task, but you only have two hours. Count the residue from dividing the sought largest common divisor by $ m $ .

输入输出格式

输入格式

The first line contains four space-separated integers $ m $ , $ l $ , $ r $ and $ k $ $ (1<=m<=10^{9}; 1<=l&lt;r<=10^{12}; 2<=k<=r-l+1) $ . Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.

输出格式

Print a single integer — the residue from dividing the sought greatest common divisor by $ m $ .

输入输出样例

输入样例 #1

10 1 8 2

输出样例 #1

3

输入样例 #2

10 1 8 3

输出样例 #2

1