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 N = 3 * (a + b);
  if (r - l >= N) {
    if (a > b)
      cout << a + (a - b);
    else
      cout << a + 1;
    return 0;
  }
  int st = 2 * (a + b);
  int pp = l / st;
  l -= pp * st;
  r -= pp * st;
  string s;
  int res = INT_MAX;
  function<void()> dfs = [&]() {
    if ((int)s.length() > r) {
      set<char> cur;
      for (int i = l; i < r + 1; i++) cur.insert(s[i]);
      res = min(res, (int)cur.size());
      return;
    }
    vector<int> cnt(26);
    int sz = s.length();
    for (int i = sz - 1; i > max(-1, sz - 1 - a); i--) cnt[s[i] - 'a'] = 1;
    for (int i = 0; i < 26; i++) {
      if (!cnt[i]) {
        s += 'a' + i;
        if ((int)s.length() == sz + a) break;
      }
    }
    for (int i = 0; i < 26; i++) {
      for (int j = 0; j < b; j++) s += 'a' + i;
      dfs();
      s.resize(s.size() - b);
    }
    s.resize(sz);
  };
  dfs();
  cout << res;
  return 0;
}
