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 mod = 1e6;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int a, b, l, r;
  cin >> a >> b >> l >> r;
  int k = (l - 1) % (a + b), ans = 0;
  r = r - l + 1;
  l = k;
  vector<int> f;
  for (int i = 0; i < a; i++) f.push_back(i);
  for (int i = 0; i < b; i++) f.push_back(a - 1);
  if (a > b) {
    for (int i = 0; i < b; i++) f.push_back(i);
    for (int i = 0; i < a - b; i++) f.push_back(a + i);
    for (int i = 0; i < b; i++) f.push_back(a + a - b - 1);
    k = a + a - b;
  } else {
    for (int i = 0; i < a - 1; i++) f.push_back(i);
    for (int i = 0; i < b + 1; i++) f.push_back(a);
    k = a + 1;
  }
  if (r >= f.size())
    ans = k;
  else {
    if (l >= a && a > b) {
      for (int i = a; i < a + b; i++) f[i] = b;
    }
    vector<int> g(k);
    for (int i = 0; i < r; i++) {
      g[f[(i + l) % f.size()]]++;
    }
    for (int i = 0; i < k; i++) {
      ans += (g[i] > 0);
    }
  }
  cout << ans << endl;
}
