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;
int club(int k) {
  int rlt = (k - 1) / (a + b);
  if (k <= rlt * (a + b) + a) return rlt * 2 + 1;
  return rlt * 2 + 2;
}
int big(int k) {
  int tag = club(k) / 2;
  if (club(k) & 1) return a + 1 + (a + b) * tag;
  return 1 + (a + b) * tag;
}
int small(int k) {
  int tag = club(k) / 2;
  if (club(k) & 1) return (a + b) * tag;
  return (a + b) * (tag - 1) + a;
}
int calc(int st, int en) {
  if (club(en) > club(st) + 5) return max(a + 1, 2 * a - b);
  if (club(en) == club(st)) {
    if (club(en) & 1) return en - st + 1;
    return 1;
  }
  if (club(en) == club(st) + 1) {
    if (club(st) & 1) return a - ((st - 1) % (a + b));
    return ((en - 1) % (a + b)) + 2;
  }
  if (club(en) == club(st) + 2) {
    int x = a - ((st - 1) % (a + b)), y = (en - 1) % (a + b) + 1;
    if (club(st) & 1) return max(min(x + y, a), max(x, y + min(x, a - b)));
    return a + 1;
  }
  return max(calc(big(st), en), calc(st, small(en)));
}
int main() {
  int le, ri;
  scanf("%d %d %d %d", &a, &b, &le, &ri);
  printf("%d\n", calc(le, ri));
}
