#include <bits/stdc++.h>
using namespace std;
const int mod = 1e9 + 7;
const double eps = 1e-6;
const int inf = 0x3f3f3f3f;
const double pi = acos(-1.0);
int v[555];
set<int> ss;
int main() {
  int a, b, l, r;
  cin >> a >> b >> l >> r;
  if (r - l + 1 >= (a + b) * 2)
    cout << a + max(a - b, 1) << endl;
  else {
    int ans = 999;
    l--;
    r--;
    for (int j = 0; j < a; j++) {
      memset(v, 0, sizeof v);
      string s = "";
      for (int i = 0; i < a; i++) {
        s.push_back(i + 'a');
      }
      for (int i = 0; i < b; i++) {
        s.push_back(j + 'a');
      }
      int len = ((int)(s).size());
      for (int i = len - a; i < len; i++) {
        v[s[i] - 'a'] = 1;
      }
      for (int i = 0, j = 0; i < a; i++) {
        while (v[j]) j++;
        s.push_back(j + 'a');
        v[j] = 1;
      }
      string str = s;
      for (int k = a; k < 26; k++) {
        s = str;
        for (int i = 0; i < b; i++) {
          s.push_back(k + 'a');
        }
        int m = (a + b) * 2;
        ss.clear();
        for (int i = l; i <= r; i++) {
          ss.insert(s[i % m]);
        }
        ans = min(ans, ((int)(ss).size()));
      }
    }
    cout << ans << endl;
  }
  return 0;
}

### Prompt

Please formulate a CPP solution to 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;
const int mod = 1e9 + 7;
const double eps = 1e-6;
const int inf = 0x3f3f3f3f;
const double pi = acos(-1.0);
int v[555];
set<int> ss;
int main() {
  int a, b, l, r;
  cin >> a >> b >> l >> r;
  if (r - l + 1 >= (a + b) * 2)
    cout << a + max(a - b, 1) << endl;
  else {
    int ans = 999;
    l--;
    r--;
    for (int j = 0; j < a; j++) {
      memset(v, 0, sizeof v);
      string s = "";
      for (int i = 0; i < a; i++) {
        s.push_back(i + 'a');
      }
      for (int i = 0; i < b; i++) {
        s.push_back(j + 'a');
      }
      int len = ((int)(s).size());
      for (int i = len - a; i < len; i++) {
        v[s[i] - 'a'] = 1;
      }
      for (int i = 0, j = 0; i < a; i++) {
        while (v[j]) j++;
        s.push_back(j + 'a');
        v[j] = 1;
      }
      string str = s;
      for (int k = a; k < 26; k++) {
        s = str;
        for (int i = 0; i < b; i++) {
          s.push_back(k + 'a');
        }
        int m = (a + b) * 2;
        ss.clear();
        for (int i = l; i <= r; i++) {
          ss.insert(s[i % m]);
        }
        ans = min(ans, ((int)(ss).size()));
      }
    }
    cout << ans << endl;
  }
  return 0;
}

```