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B. The Golden Age

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputUnlucky 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.

Input

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

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

2 3 1 10

Output

1

Input

3 5 10 22

Output

8

Input

2 3 3 5

Output

0

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].

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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