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 main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  long long a, b, l, r;
  cin >> a >> b >> l >> r;
  string s(a, ' ');
  iota(begin(s), end(s), 'a');
  int max_answer = (a <= b) ? a + 1 : 2 * a - b;
  set<char> vis;
  l--, r--;
  deque<char> arr;
  for (int i = l; i <= r and int(vis.size()) < max_answer; i++) {
    if (i < a) {
      char ch = 'a' + i;
      arr.push_back(ch);
      vis.insert(ch);
    } else if (i % (a + b) < a) {
      set<char> used(begin(arr), end(arr));
      for (char ch = 'a'; ch <= 'z'; ch++) {
        if (used.count(ch)) continue;
        arr.push_back(ch);
        vis.insert(ch);
        break;
      }
    } else {
      char ch = arr.empty() ? 'a' : arr.back();
      arr.push_back(ch);
      vis.insert(ch);
      while (int(arr.size()) > a) arr.pop_front();
    }
  }
  cout << int(vis.size()) << '\n';
  return (0);
}
