## Educational Codeforces Round 22.B 暴力

• 时间：2017-07-08
• 分类：ASP.NET
• 2028 人浏览
[导读]B. The Golden Agetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputUn

B. The Golden Age time limit per test 1 second memory limit per test 256 megabytes input standard input output standard output

Unlucky year in Berland is such a year that its number n can be represented as n = xa + yb, 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 = 20 + 31, 17 = 23 + 32 = 24 + 30) 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.

Input

The first line contains four integer numbers xyl and r (2 ≤ x, y ≤ 1018, 1 ≤ l ≤ r ≤ 1018).

Output

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.

Examples input

output

input

output

input

output

Note

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].

题意：给定一个a和b 如果满足 pow(a,i)+pow(b,j),就说这个数不幸运 求一个区间内最大的没有不幸运数的区间。