#include <bits/stdc++.h>
using namespace std;
int a, b, l, r, ans, T;
char s[200];
bool vis[27];
int dfs(char cp) {
  int count = 0;
  for (int i = 0; i < a; i++) s[i] = ('a' + i);
  for (int i = a; i < a + b; i++) s[i] = cp;
  memset(vis, false, sizeof(vis));
  for (int i = b; i < a + b; i++) vis[s[i] - 'a'] = true;
  int sta = a + b, ed = 0;
  while (sta < 2 * a + b) {
    while (vis[ed]) ed++;
    s[sta] = ed + 'a';
    sta++, ed++;
  }
  for (int i = 2 * a + b; i < T; i++) s[i] = s[i - 1];
  memset(vis, false, sizeof(vis));
  if (l <= r) {
    for (int i = l; i <= r; i++) {
      if (!vis[s[i] - 'a']) {
        count++, vis[s[i] - 'a'] = true;
      }
    }
  } else {
    for (int i = 0; i <= r; i++) {
      if (!vis[s[i] - 'a']) {
        count++, vis[s[i] - 'a'] = true;
      }
    }
    for (int i = l; i < T; i++) {
      if (!vis[s[i] - 'a']) {
        count++, vis[s[i] - 'a'] = true;
      }
    }
  }
  return count;
}
int main() {
  cin >> a >> b >> l >> r;
  l--, r--;
  if (a <= b)
    ans = a + 1;
  else
    ans = 2 * a - b;
  T = 2 * (a + b);
  if (r - l >= T)
    ;
  else {
    r %= T, l %= T;
    for (int i = 0; i < a; i++) {
      ans = min(dfs('a' + i), ans);
    }
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Please create a solution in CPP 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;
int a, b, l, r, ans, T;
char s[200];
bool vis[27];
int dfs(char cp) {
  int count = 0;
  for (int i = 0; i < a; i++) s[i] = ('a' + i);
  for (int i = a; i < a + b; i++) s[i] = cp;
  memset(vis, false, sizeof(vis));
  for (int i = b; i < a + b; i++) vis[s[i] - 'a'] = true;
  int sta = a + b, ed = 0;
  while (sta < 2 * a + b) {
    while (vis[ed]) ed++;
    s[sta] = ed + 'a';
    sta++, ed++;
  }
  for (int i = 2 * a + b; i < T; i++) s[i] = s[i - 1];
  memset(vis, false, sizeof(vis));
  if (l <= r) {
    for (int i = l; i <= r; i++) {
      if (!vis[s[i] - 'a']) {
        count++, vis[s[i] - 'a'] = true;
      }
    }
  } else {
    for (int i = 0; i <= r; i++) {
      if (!vis[s[i] - 'a']) {
        count++, vis[s[i] - 'a'] = true;
      }
    }
    for (int i = l; i < T; i++) {
      if (!vis[s[i] - 'a']) {
        count++, vis[s[i] - 'a'] = true;
      }
    }
  }
  return count;
}
int main() {
  cin >> a >> b >> l >> r;
  l--, r--;
  if (a <= b)
    ans = a + 1;
  else
    ans = 2 * a - b;
  T = 2 * (a + b);
  if (r - l >= T)
    ;
  else {
    r %= T, l %= T;
    for (int i = 0; i < a; i++) {
      ans = min(dfs('a' + i), ans);
    }
  }
  cout << ans << endl;
  return 0;
}

```