CF819A.Mister B and Boring Game

普及/提高-

通过率：0%

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题目描述

Sometimes 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 $1$ .

输入格式

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.

输出格式

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

输入输出样例

输入#1
```
1 1 1 8
```
输出#1
```
2
```
输入#2
```
4 2 2 6
```
输出#2
```
3
```
输入#3
```
3 7 4 6
```
输出#3
```
1
```

说明/提示

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 $1$ .

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