The Golden Age

题意翻译

大意：给你一个区间 $[L，R]$，让你求出在这个区间内最长的子区间的长度，使得这个区间内的每一个整数 $n∈[L，R]$ 都不能表达为 $n=x^a+y^b$，如果不存在这样的区间或其长度为 $0$，输出 $0$。 其中 $a,b$ 都为非负整数，$1 \le L \le R \le 10^{18}$，$2 \le x,y \le 10^{18}$，$x,y,L,R$ 都为整数。 输入：仅一行，分别是 $x,y,L,R$。 输出：仅一行，即满足条件的最大子区间的长度。 样例说明：对于第一组数据，不幸年是2,3,4,5,7,9，所以最长为[1,1],[6,6],[8,8]，length为1 对于第二组数据，最长区间为[15,22],length为8 **（注意：对于不同的x,y，同一个[L,R]的长度可能不一样）**

题目描述

Unlucky year in Berland is such a year that its number $ n $ can be represented as $ n=x^{a}+y^{b} $ , where $ a $ and $ b $ are non-negative integer numbers. For example, if $ x=2 $ and $ y=3 $ then the years 4 and 17 are unlucky ( $ 4=2^{0}+3^{1} $ , $ 17=2^{3}+3^{2}=2^{4}+3^{0} $ ) and year 18 isn't unlucky as there is no such representation for it. Such interval of years that there are no unlucky years in it is called The Golden Age. You should write a program which will find maximum length of The Golden Age which starts no earlier than the year $ l $ and ends no later than the year $ r $ . If all years in the interval $ [l,r] $ are unlucky then the answer is 0.

输入输出格式

输入格式

The first line contains four integer numbers $ x $ , $ y $ , $ l $ and $ r $ ( $ 2<=x,y<=10^{18} $ , $ 1<=l<=r<=10^{18} $ ).

输出格式

Print the maximum length of The Golden Age within the interval $ [l,r] $ . If all years in the interval $ [l,r] $ are unlucky then print 0.

输入输出样例

输入样例 #1

2 3 1 10

输出样例 #1

1

输入样例 #2

3 5 10 22

输出样例 #2

8

输入样例 #3

2 3 3 5

输出样例 #3

0

说明

In the first example the unlucky years are 2, 3, 4, 5, 7, 9 and 10. So maximum length of The Golden Age is achived in the intervals $ [1,1] $ , $ [6,6] $ and $ [8,8] $ . In the second example the longest Golden Age is the interval $ [15,22] $ .