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;
const int MAX_TAKE = 2000;
int a, b, l, r;
string Alien(const string& w) {
  set<char> used;
  for (int i = ((int)(w).size()) - a; i < ((int)(w).size()); ++i)
    used.insert(w[i]);
  string tmp;
  for (char c = 'a'; c <= 'z'; ++c) {
    if (!used.count(c)) tmp += c;
    if (((int)(tmp).size()) == a) return tmp;
  }
}
int Diff(const string& w, int l, int r) {
  set<char> used;
  for (int i = l; i <= r; ++i) used.insert(w[i]);
  return ((int)(used).size());
}
int main() {
  cin >> a >> b >> l >> r;
  --l, --r;
  int take = min(MAX_TAKE, r - l + 1);
  l %= a + b;
  int ans = 1E9;
  string s;
  for (int i = 0; i < a; ++i) s += char('a' + i);
  while (((int)(s).size()) < 2 * MAX_TAKE) {
    for (int i = 0; i < b; ++i) s += 'z';
    s += Alien(s);
  }
  (ans) = min((ans), (Diff(s, l, l + take - 1)));
  for (int p = 1; p <= a; ++p) {
    s = "";
    for (int i = 0; i < a; ++i) s += char('a' + i);
    while (((int)(s).size()) < 2 * MAX_TAKE) {
      char t = s[((int)(s).size()) - p];
      for (int i = 0; i < b; ++i) s += t;
      s += Alien(s);
    }
    (ans) = min((ans), (Diff(s, l, l + take - 1)));
  }
  cout << ans << '\n';
  return 0;
}
