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;
bool used[128];
int main() {
  cin >> A >> B >> L >> R;
  L--, R--;
  int maxans = A <= B ? A + 1 : A + A - B;
  int ans = -1234;
  queue<int> q;
  for (int i = L; i <= R; i++) {
    if (i < A) {
      used[i] = true;
      q.push(i);
    } else if (i % (A + B) < A) {
      int c;
      {
        queue<int> cpy = q;
        set<int> S;
        while (!cpy.empty()) {
          int x = cpy.front();
          cpy.pop();
          S.insert(x);
        }
        c = 0;
        for (int x : S)
          if (c == x) c++;
      }
      used[c] = true;
      q.push(c);
    } else {
      int c = q.empty() ? 0 : q.back();
      used[c] = true;
      q.push(c);
      while (q.size() > A) q.pop();
    }
    ans = 0;
    for (int x = 0; x < 100; x++) ans += used[x];
    if (ans == maxans) break;
  }
  assert(ans >= 1);
  cout << ans << endl;
  return 0;
}
