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_base::sync_with_stdio(false);
  cin.tie(nullptr);
  int a, b, l, r;
  cin >> a >> b >> l >> r;
  --l;
  int ans = r - l;
  for (auto k : {0, 1}) {
    string s;
    for (int i = 0; i < 4; ++i) {
      set<char> used;
      for (int j = 1; j <= min(a, int(s.size())); ++j) {
        used.insert(s[int(s.size()) - j]);
      }
      char c = 'a';
      for (int j = 0; j < a; ++j) {
        while (used.count(c) != 0) {
          ++c;
        }
        s += c;
        ++c;
      }
      s += max(int('a'), s.back() - k);
      for (int j = 1; j < b; ++j) {
        s += s.back();
      }
    }
    int m = s.size();
    if (r - l >= m) {
      l = 0;
      r = m - 1;
    }
    set<char> seen;
    for (int i = l; i % m != r % m; ++i) {
      seen.insert(s[i % m]);
    }
    ans = min(ans, int(seen.size()));
  }
  cout << ans << "\n";
}
