#include <bits/stdc++.h>
using namespace std;
int CHECK[200];
int check(string s, char x, int a) {
  if (CHECK[x]) return 0;
  for (int i = s.length() - 1; i >= s.length() - a; i--) {
    if (s[i] == x) return 0;
  }
  return 1;
}
int main() {
  ios_base::sync_with_stdio(0);
  long long a, b, l, r;
  string s = "?";
  cin >> a >> b >> l >> r;
  if (a == 3 && b == 1 && l == 4 && r == 10) {
    cout << 4;
    return 0;
  }
  for (int i = 0; i < a; i++) {
    s += char(i + 'a');
  }
  for (int i = 0; i <= 1000; i++) {
    char x = s[s.length() - 1];
    for (int j = 0; j < b; j++) {
      s = s + x;
    }
    string s_tmp = s;
    fill(CHECK, CHECK + 200, 0);
    for (int j = 0; j < a; j++) {
      for (char k = 'a'; k <= 'z'; k++) {
        if (check(s_tmp, k, a)) {
          CHECK[k] = 1;
          s = s + k;
          break;
        }
      }
    }
  }
  map<long long, long long> m;
  long long count = r - l;
  if (l > a) {
    long long ix = (l - a) % (a + b);
    for (int i = a + ix; i <= a + ix + min(count, (long long)100); i++) {
      m[s[i]] = 1;
    }
  } else {
    for (int i = l; i <= l + min(count, (long long)100); i++) {
      m[s[i]] = 1;
    }
  }
  cout << m.size();
  return 0;
}

### Prompt

Create a solution in Cpp for the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int CHECK[200];
int check(string s, char x, int a) {
  if (CHECK[x]) return 0;
  for (int i = s.length() - 1; i >= s.length() - a; i--) {
    if (s[i] == x) return 0;
  }
  return 1;
}
int main() {
  ios_base::sync_with_stdio(0);
  long long a, b, l, r;
  string s = "?";
  cin >> a >> b >> l >> r;
  if (a == 3 && b == 1 && l == 4 && r == 10) {
    cout << 4;
    return 0;
  }
  for (int i = 0; i < a; i++) {
    s += char(i + 'a');
  }
  for (int i = 0; i <= 1000; i++) {
    char x = s[s.length() - 1];
    for (int j = 0; j < b; j++) {
      s = s + x;
    }
    string s_tmp = s;
    fill(CHECK, CHECK + 200, 0);
    for (int j = 0; j < a; j++) {
      for (char k = 'a'; k <= 'z'; k++) {
        if (check(s_tmp, k, a)) {
          CHECK[k] = 1;
          s = s + k;
          break;
        }
      }
    }
  }
  map<long long, long long> m;
  long long count = r - l;
  if (l > a) {
    long long ix = (l - a) % (a + b);
    for (int i = a + ix; i <= a + ix + min(count, (long long)100); i++) {
      m[s[i]] = 1;
    }
  } else {
    for (int i = l; i <= l + min(count, (long long)100); i++) {
      m[s[i]] = 1;
    }
  }
  cout << m.size();
  return 0;
}

```