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 ≤ 109) — 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.
#include <bits/stdc++.h>
using namespace std;
int a, b, st, en;
int tag(int k) {
  int rlt = (k - 1) / (a + b);
  if ((k - 1) % (a + b) < a) return rlt * 2 + 1;
  return rlt * 2 + 2;
}
int solve(int st, int en) {
  int u = tag(st), v = tag(en);
  if (v > u + 4) return max(a + 1, 2 * a - b);
  if (v == u) return u & 1 ? en - st + 1 : 1;
  if (v == u + 1)
    return u & 1 ? a - ((st - 1) % (a + b)) : ((en - 1) % (a + b)) + 2;
  if (v == u + 2) {
    int x = a - ((st - 1) % (a + b)), y = (en - 1) % (a + b) + 1;
    return u & 1 ? max(min(x + y, a), max(x, y + max(1, min(x, a - b))))
                 : a + 1;
  }
  return max(
      solve(a * (tag(st) & 1) + 1 + (a + b) * (tag(st) >> 1), en),
      solve(st, (a + b) * ((tag(en) - 1) >> 1) + a * ((tag(en) - 1) & 1)));
}
int main() {
  scanf("%d%d%d%d", &a, &b, &st, &en);
  printf("%d\n", solve(st, en));
}
