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;
signed main() {
  std::ios::sync_with_stdio(false);
  cin.tie(0);
  int a, b, l, r;
  cin >> a >> b >> l >> r;
  l--;
  if (r - l == 1) {
    cout << "1\n";
    return 0;
  }
  if (r - l >= 2 * a + 2 * b) {
    if (b < a)
      cout << 2 * a - b << "\n";
    else
      cout << a + 1 << "\n";
    return 0;
  }
  vector<int> arr(2 * a + 2 * b);
  l %= arr.size();
  r %= arr.size();
  int p = a - 1;
  if (l > r and r > 0) p = min(r - 1, a - 1);
  for (int i = 0; i < a; i++) arr[i] = i;
  for (int i = a; i < a + b; i++) arr[i] = p;
  int w = min(b, a - 1);
  for (int i = 0; i < w; i++) arr[i + a + b] = i;
  for (int i = 0; i < a - w; i++) arr[i + a + b + w] = i + a;
  for (int i = 2 * a + b; i < 2 * a + 2 * b; i++) arr[i] = arr[2 * a + b - 1];
  vector<bool> st(30);
  for (int i = l; i != r; i = (i + 1) % arr.size()) {
    st[arr[i]] = true;
  }
  int res = 0;
  for (bool e : st) res += e;
  cout << res << "\n";
}
