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 $1$.

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 $*s*$.

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 $1$.