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 ab;
bool vis[32];
int ans = 1e9;
void dfs(int p, vector<int> letters) {
  if (p > r || p > l + 2 * ab) {
    int s = 0;
    while (p - letters.size() + s < l) {
      s++;
    }
    set<int> Set;
    for (int i = s; i < letters.size(); i++) {
      Set.insert(letters[i]);
    }
    ans = min(ans, (int)Set.size());
    return;
  }
  while (p + ab < l) {
    p += ab;
  }
  int pos = p % ab;
  if (pos == 0) {
    bool ban[26];
    memset(ban, 0, sizeof(ban));
    for (int i = 1; i <= a; i++) {
      if (letters.size() < i) break;
      ban[letters[letters.size() - i]] = 1;
    }
    int ai = 0;
    for (int j = 0; j < a; j++, p++) {
      if (p > r) break;
      while (ban[ai]) {
        ai++;
      }
      letters.push_back(ai++);
    }
    dfs(p, letters);
  } else {
    for (int i = 1; i <= a; i++) {
      if (letters.size() < i) break;
      vector<int> nl = letters;
      for (int j = 1; j <= b; j++) {
        nl.push_back(letters[letters.size() - i]);
      }
      dfs(p + b, nl);
    }
  }
}
int main() {
  cin >> a >> b >> l >> r;
  l--;
  r--;
  ab = a + b;
  vector<int> v;
  dfs(0, v);
  cout << ans << endl;
  return 0;
}
