#include <bits/stdc++.h>
using namespace std;
char str[30][100];
int visit[100];
int len, tot, kind, a, b, l, r;
void prepare() {
  tot = (a <= b ? a + 1 : 2 * a - b);
  len = ((a + b) << 1);
  if (b >= a) {
    kind = 1;
    for (int i = 1; i <= a; ++i) str[1][i] = 'a' + i - 1;
    for (int i = a + 1; i <= a + b; ++i) str[1][i] = str[1][a];
    for (int i = a + b; i > b; --i) visit[str[1][i] - 'a'] = 1;
    for (int i = a + b + 1, j = 0; i <= 2 * a + b; ++i) {
      while (visit[j]) ++j;
      str[1][i] = 'a' + j;
      visit[j] = 1;
    }
    for (int i = a + b + a + 1; i <= a + b + a + b; ++i)
      str[1][i] = str[1][a + b + a];
    for (int i = 2 * (a + b) + 1; i <= 4 * (a + b); ++i)
      str[1][i] = str[1][i - 2 * (a + b)];
    str[1][4 * (a + b) + 1] = '\0';
  } else {
    kind = a - b;
    for (int k = 1; k <= a - b; ++k) {
      memset(visit, 0, sizeof(visit));
      for (int i = 1; i <= a; ++i) str[k][i] = 'a' + i - 1;
      for (int i = a + 1; i <= a + b; ++i) str[k][i] = str[k][k + b];
      for (int i = a + b; i > b; --i) visit[str[k][i] - 'a'] = 1;
      for (int i = a + b + 1, j = 0; i <= 2 * a + b; ++i) {
        while (visit[j]) ++j;
        str[k][i] = 'a' + j;
        visit[j] = 1;
      }
      for (int i = a + b + a + 1; i <= a + b + a + b; ++i)
        str[k][i] = str[k][a + b + a];
      for (int i = 2 * (a + b) + 1; i <= 4 * (a + b); ++i)
        str[k][i] = str[k][i - 2 * (a + b)];
      str[k][4 * (a + b) + 1] = '\0';
    }
  }
}
int main() {
  scanf("%d%d%d%d", &a, &b, &l, &r);
  prepare();
  if (r - l >= len)
    printf("%d\n", tot);
  else {
    r = (r - 1) % len + 1;
    l = (l - 1) % len + 1;
    if (r < l) r += len;
    int ans = 100;
    memset(visit, 0, sizeof(visit));
    for (int k = 1; k <= kind; ++k) {
      int temp = 0;
      memset(visit, 0, sizeof(visit));
      for (int i = l; i <= r; ++i) {
        if (visit[str[k][i] - 'a'] == 0) {
          ++temp;
          visit[str[k][i] - 'a'] = 1;
        }
      }
      ans = min(temp, ans);
    }
    printf("%d\n", ans);
  }
  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;
char str[30][100];
int visit[100];
int len, tot, kind, a, b, l, r;
void prepare() {
  tot = (a <= b ? a + 1 : 2 * a - b);
  len = ((a + b) << 1);
  if (b >= a) {
    kind = 1;
    for (int i = 1; i <= a; ++i) str[1][i] = 'a' + i - 1;
    for (int i = a + 1; i <= a + b; ++i) str[1][i] = str[1][a];
    for (int i = a + b; i > b; --i) visit[str[1][i] - 'a'] = 1;
    for (int i = a + b + 1, j = 0; i <= 2 * a + b; ++i) {
      while (visit[j]) ++j;
      str[1][i] = 'a' + j;
      visit[j] = 1;
    }
    for (int i = a + b + a + 1; i <= a + b + a + b; ++i)
      str[1][i] = str[1][a + b + a];
    for (int i = 2 * (a + b) + 1; i <= 4 * (a + b); ++i)
      str[1][i] = str[1][i - 2 * (a + b)];
    str[1][4 * (a + b) + 1] = '\0';
  } else {
    kind = a - b;
    for (int k = 1; k <= a - b; ++k) {
      memset(visit, 0, sizeof(visit));
      for (int i = 1; i <= a; ++i) str[k][i] = 'a' + i - 1;
      for (int i = a + 1; i <= a + b; ++i) str[k][i] = str[k][k + b];
      for (int i = a + b; i > b; --i) visit[str[k][i] - 'a'] = 1;
      for (int i = a + b + 1, j = 0; i <= 2 * a + b; ++i) {
        while (visit[j]) ++j;
        str[k][i] = 'a' + j;
        visit[j] = 1;
      }
      for (int i = a + b + a + 1; i <= a + b + a + b; ++i)
        str[k][i] = str[k][a + b + a];
      for (int i = 2 * (a + b) + 1; i <= 4 * (a + b); ++i)
        str[k][i] = str[k][i - 2 * (a + b)];
      str[k][4 * (a + b) + 1] = '\0';
    }
  }
}
int main() {
  scanf("%d%d%d%d", &a, &b, &l, &r);
  prepare();
  if (r - l >= len)
    printf("%d\n", tot);
  else {
    r = (r - 1) % len + 1;
    l = (l - 1) % len + 1;
    if (r < l) r += len;
    int ans = 100;
    memset(visit, 0, sizeof(visit));
    for (int k = 1; k <= kind; ++k) {
      int temp = 0;
      memset(visit, 0, sizeof(visit));
      for (int i = l; i <= r; ++i) {
        if (visit[str[k][i] - 'a'] == 0) {
          ++temp;
          visit[str[k][i] - 'a'] = 1;
        }
      }
      ans = min(temp, ans);
    }
    printf("%d\n", ans);
  }
  return 0;
}

```