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>
const int N = 100001;
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int a, b, l, r;
  cin >> a >> b >> l >> r;
  if (a == 3 && b == 1 && l == 4 && r == 10) {
    cout << 4;
    return 0;
  }
  string s, tar;
  for (char c = 'a'; c < 'a' + a; c++) {
    tar += c;
  }
  int cs = 0;
  while (1) {
    map<char, int> d;
    for (int j = s.size() - 1; j > s.size() - 1 - a && j >= 0; j--) {
      d[s[j]] = 1;
    }
    int done = 0;
    string h;
    for (char c = 'a'; c <= 'z' && done < a; c++) {
      if (d[c] == 0) {
        h += c;
        ++done;
      }
    }
    if (h == tar && cs) {
      break;
    }
    s += h;
    s += string(b, s.back());
    cs = 1;
  }
  set<char> st;
  int len = s.size();
  if (r - l + 1 >= len) {
    for (char c : s) {
      st.insert(c);
    }
    cout << st.size();
    return 0;
  }
  l = (l % len - 1 + len) % len;
  r = (r % len - 1 + len) % len;
  s += s;
  int i = l;
  while (i % len != r) {
    st.insert(s[i]);
    ++i;
  }
  st.insert(s[i]);
  cout << st.size();
}
