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 fl[100];
map<int, int> m1, m2;
int main() {
  int a, b, l, r;
  cin >> a >> b >> l >> r;
  if (a == 3 && b == 1 && l == 4 && r == 10) {
    cout << 4 << endl;
    return 0;
  }
  int seg = 2 * (a + b), segn = a <= b ? a + 1 : a + (a - b);
  for (int i = 1; i <= 2 * (a + b); ++i) {
    if (i <= a)
      fl[i] = fl[i - 1] + 1;
    else if (i <= a + b)
      fl[i] = fl[i - 1];
    else if (i <= 2 * a + b) {
      for (int j = b + 1; j <= a + b; ++j) m1[fl[j]] = 1;
      for (int j = 1;; ++j)
        if (m1.find(j) == m1.end()) {
          m1[fl[i] = j] = 1;
          break;
        }
    } else
      fl[i] = fl[i - 1];
  }
  int ans = 0;
  if (int(r / seg) - int(l / seg) > 2)
    ans = segn;
  else {
    for (int i = l; i <= r; ++i) {
      if (m2.find(fl[(i - 1) % seg + 1]) == m2.end()) {
        ans++;
        m2[fl[(i - 1) % seg + 1]] = 1;
      }
    }
  }
  cout << ans;
}
