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(int argc, char** argv) {
  long long a, b;
  long long l, r;
  cin >> a >> b;
  cin >> l >> r;
  l = l - 1;
  r = r - 1;
  r = r - (l / (2 * (a + b))) * (2 * (a + b));
  l = l % (2 * (a + b));
  char rep_1, rep_2;
  if (l < a) {
    rep_1 = 'a' + a - 1;
  } else {
    rep_1 = 'a' + min(b, a - 1LL);
  }
  if (l < 2 * a + b) {
    rep_2 = 'a' + a + max(a - b - 1, 0LL);
  } else {
    rep_2 = 'a' + a + min(0LL, max(a - b - 1, 0LL));
  }
  set<char> result_set;
  for (int k = 0; k < 4 * (a + b); ++k) {
    int i = k % (2 * (a + b));
    char cur;
    if (i < a) {
      cur = 'a' + i;
    } else if ((i >= a) && (i < a + b)) {
      cur = rep_1;
    } else if ((i >= a + b) && (i < 2 * a + b - max(1LL, a - b))) {
      cur = 'a' + i - (a + b);
    } else if ((i >= 2 * a + b - max(1LL, a - b)) && (i < 2 * a + b)) {
      cur = 'a' + a + i - (2 * a + b - max(1LL, a - b));
    } else {
      cur = rep_2;
    }
    if ((k >= l) && (k <= r)) {
      result_set.insert(cur);
    }
  }
  cout << result_set.size() << endl;
}
