CF819A.Mister B and Boring Game

Unfortunately, a mistake was found in the proof of the author's solution to this problem. Currently, we don't know the absolutely correct solution. However, you can solve this task, but if your solution passes all the tests, it is not guaranteed to be correct. If your solution has passed all the tests, and you are sure that it is correct, you can write to one of the contest authors about it.

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.

很遗憾，本题作者解法的证明中被发现存在一处错误。目前我们尚不清楚绝对正确的解法。不过，你仍然可以尝试解决本题；但即使你的解法通过了所有测试用例，也不能保证其正确性。如果你的解法已通过全部测试，并且你确信它是正确的，你可以联系本次比赛的一位出题人。

有时，Mr. B 会在晚上空闲时不知该做些什么。幸运的是，Mr. B 发现了一款新游戏，玩家可以在其中与外星人对战。

该游戏中的所有角色均为小写英文字母。游戏中有两位玩家：Mr. B 与其对手。

初始时，双方拥有一个字符串 $ s $，它由前 $ a $ 个按字母顺序排列的英文小写字母组成（例如，若 $ a = 5 $，则 $ s $ 为 "abcde"）。

双方轮流在字符串 $ s $ 末尾添加字母，Mr. B 先手。

Mr. B 每次必须恰好添加 $ b $ 个字母，这些字母可任意选择；而他的对手每次则恰好添加 $ a $ 个字母。

Mr. B 很快意识到，他的对手其实是一台计算机，且采用一种简单的算法：计算机在每一轮中，先考察字符串 $ s $ 的长度为 $ a $ 的后缀，然后生成一个长度为 $ a $ 的字符串 $ t $，使得 $ t $ 中所有字母互不相同，且均不出现在该后缀中；若存在多个满足条件的 $ t $，则选择字典序最小的那个（例如，若 $ a = 4 $，当前后缀为 "bfdd"，则计算机选择的 $ t $ 为 "aceg"）。随后，将所选的字符串 $ t $ 追加到 $ s $ 的末尾。

Mr. B 很快觉得这个游戏很无聊，于是提出了如下问题：字符串 $ s $ 在位置 $ l $ 到 $ r $（含端点）这一区间内，不同字母的最少可能个数是多少？字符串 $ s $ 的字符位置编号从 1 开始。

First and only line contains four space-separated integers: a, b, l and r (1 ≤ a, b ≤ 12, 1 ≤ l ≤ r ≤ 109) — the numbers of letters each player appends and the bounds of the segment.

第一行且唯一一行包含四个以空格分隔的整数：$a$、$b$、$l$ 和 $r$（$1 ≤ a, b ≤ 12$，$1 ≤ l ≤ r ≤ 10^9$）——分别表示两名玩家每次追加的字母数量以及区间的边界。

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

输出一个整数——字符串 $s$ 中从位置 $l$ 到位置 $r$（包含端点）的子串内，最少可能包含的不同字母数量。

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.

在第一个样例测试中，一种最优策略生成的字符串为 $s = \text{“abababab...”}$，因此答案为 2。

在第二个样例测试中，可得到字符串 $s = \text{“abcdbcaefg...”}$，所选子段为 “bcdbc”，因此答案为 3。

在第三个样例测试中，可得到字符串 $s = \text{“abczzzacad...”}$，所选子段为 “zzz”，因此答案为 1。