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A. Mister B and Boring Game

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputSometimes Mister B has free evenings when he doesn't know what to do. Fortunately, Mister B found a new game, where the player can play against aliens.

All characters in this game are lowercase English letters. There are two players: Mister B and his competitor.

Initially the players have a string *s* consisting of the first *a* English letters in alphabetical order (for example, if *a* = 5, then *s* equals to "abcde").

The players take turns appending letters to string *s*. Mister B moves first.

Mister B must append exactly *b* letters on each his move. He can arbitrary choose these letters. His opponent adds exactly *a* letters on each move.

Mister B quickly understood that his opponent was just a computer that used a simple algorithm. The computer on each turn considers the suffix of string *s* of length *a* and generates a string *t* of length *a* such that all letters in the string *t* are distinct and don't appear in the considered suffix. From multiple variants of *t* lexicographically minimal is chosen (if *a* = 4 and the suffix is "bfdd", the computer chooses string *t* equal to "aceg"). After that the chosen string *t* is appended to the end of *s*.

Mister B soon found the game boring and came up with the following question: what can be the minimum possible number of different letters in string *s* on the segment between positions *l* and *r*, inclusive. Letters of string *s* are numerated starting from 1.

Input

First and only line contains four space-separated integers: *a*, *b*, *l* and *r* (1 ≤ *a*, *b* ≤ 12, 1 ≤ *l* ≤ *r* ≤ 10^{9}) — the numbers of letters each player appends and the bounds of the segment.

Output

Print one integer — the minimum possible number of different letters in the segment from position *l* to position *r*, inclusive, in string *s*.

Examples

Input

1 1 1 8

Output

2

Input

4 2 2 6

Output

3

Input

3 7 4 6

Output

1

Note

In the first sample test one of optimal strategies generate string *s* = "abababab...", that's why answer is 2.

In the second sample test string *s* = "abcdbcaefg..." can be obtained, chosen segment will look like "bcdbc", that's why answer is 3.

In the third sample test string *s* = "abczzzacad..." can be obtained, chosen, segment will look like "zzz", that's why answer is 1.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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