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;
const int maxn = 100 + 5;
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 line[maxn];
  if (r - l + 1 >= 2 * (a + b)) {
    if (a <= b)
      cout << a + 1 << endl;
    else
      cout << 2 * a - b << endl;
    return 0;
  }
  int d = r - l;
  l--;
  l %= (a + b);
  r = l + d;
  memset(line, 0, sizeof(line));
  for (int i = 0; i < a; i++) line[i] = i + 1;
  int cur = 1;
  for (int i = a; i <= 2 * (a + b); i++) {
    if (i % (a + b) == a) {
      int j = i;
      while (i != j + b - 1) line[i++] = line[j - 1];
      line[i] = line[j - 1];
      cur = 1;
    } else {
      int j = i;
      while (i != j + a) {
        bool ok = false;
        while (!ok) {
          int oo = true;
          for (int z = j - 1; z >= 0 && z >= j - a; z--) {
            if (cur == line[z]) {
              oo = false;
              break;
            }
          }
          if (oo) {
            line[i] = cur++;
            ok = true;
          } else
            cur++;
        }
        i++;
      }
      i--;
    }
  }
  set<int> box;
  for (int i = l; i <= r; i++) box.insert(line[i]);
  cout << box.size() << endl;
  return 0;
}
