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() {
  vector<string> v;
  int a, b, len;
  char c;
  long l, r, n, min = 100, l2, r2;
  cin >> a >> b >> l2 >> r2;
  string s, newstr, suffix, s2;
  for (c = 'a'; c < 'a' + a; c++) s2 += c;
  n = 2 * (a + b);
  if (r2 - l2 + 1 >= n) {
    if (b >= a)
      cout << a + 1;
    else
      cout << a + a - b;
  } else {
    int t = a - b;
    if (t < 1) t = 1;
    for (int t1 = 1; t1 <= t; t1++)
      for (int t2 = 1; t2 <= t; t2++) {
        s = s2;
        len = s.length();
        for (int j = 0; j < b; j++) s += s[len - t1];
        len = s.length();
        c = 'a';
        suffix = s.substr(len - a, a);
        for (int k = 0; k < a; k++) {
          while (suffix.find(c) != -1) c++;
          s += c;
          c++;
        }
        len = s.length();
        for (int j = 0; j < b; j++) s += s[len - t2];
        newstr = "";
        l = l2 % n;
        r = r2 % n;
        if (r < l) r += n;
        for (int i = l - 1; i < r; i++) {
          int p = i % n;
          if (newstr.find(s[p]) == -1) newstr += s[p];
        }
        if (newstr.length() < min) min = newstr.length();
      }
    cout << min;
  }
  return 0;
}
