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, l, r;
int main() {
  cin >> a >> b >> l >> r;
  l--;
  r--;
  int pl = l % (a + b);
  int pr = r % (a + b);
  int cl = l / (a + b);
  int cr = r / (a + b);
  if (b >= a) {
    if (cr > cl + 1) {
      printf("%d\n", a + 1);
    } else if (cr == cl + 1) {
      int le = max(1, a - pl);
      int ri = min(a, pr + 1);
      int ans = min(a, le + ri);
      if (ri == a) ans++;
      printf("%d\n", ans);
    } else {
      printf("%d\n", min(pr - pl + 1, max(1, a - pl)));
    }
  } else {
    int minus = a - b;
    if (cr > cl + 2) {
      printf("%d\n", minus + a);
    } else if (cr == cl + 2) {
      printf("%d\n", a + max(1, min(minus, max(pr + 1 - a + minus, 0) +
                                               max(0, a - pl))));
    } else if (cr == cl + 1) {
      int ans = max(1, min(minus, a - pl)) + min(a, pr + 1);
      printf("%d\n", ans);
    } else {
      printf("%d\n", min(pr - pl + 1, max(1, a - pl)));
    }
  }
  return 0;
}
