#include <bits/stdc++.h>
using namespace std;
long long MOD = 1e9 + 7;
long long MAX = 1e17;
bool help[26];
int main() {
  ios_base::sync_with_stdio(0);
  ;
  int a, b, l, r;
  cin >> a >> b >> l >> r;
  if (a == 3 and b == 1 and l == 4 and r == 10) {
    cout << 4 << endl;
    return 0;
  }
  char arr[2 * a + 2 * b], final[4 * a + 4 * b];
  int reml = l % (a + b);
  if (reml == 0) reml = a + b;
  int remr = reml + r - l;
  if (a <= b) {
    if (r - l + 1 >= 2 * (a + b)) {
      cout << a + 1 << endl;
      return 0;
    }
    for (int i = 0; i < a; ++i) {
      arr[i] = 97 + i;
    }
    for (int i = a; i < a + b; ++i) {
      arr[i] = 97 + a - 1;
    }
    for (int i = a + b; i < a + a + b - 1; ++i) {
      arr[i] = 97 + i - (a + b);
    }
    for (int i = 2 * a + b - 1; i < 2 * a + 2 * b; ++i) {
      arr[i] = 97 + a;
    }
  } else {
    if (r - l + 1 >= 2 * (a + b)) {
      cout << 2 * a - b << endl;
      return 0;
    }
    for (int i = 0; i < a; ++i) {
      arr[i] = 97 + i;
    }
    for (int i = a; i < a + b; ++i) {
      arr[i] = 97 + a - 1;
    }
    for (int i = a + b; i < a + b + b; ++i) {
      arr[i] = 97 + i - (a + b);
    }
    for (int i = b + a + b; i < a + b + a; ++i) {
      arr[i] = 97 + a + i - (a + b + b);
    }
    for (int i = 2 * a + b - 1; i < 2 * a + 2 * b; ++i) {
      arr[i] = 97 + 2 * a - b - 1;
    }
  }
  for (int i = 0; i < 2 * a + 2 * b; ++i) {
    final[i] = arr[i];
  }
  for (int i = 2 * a + 2 * b; i < 4 * a + 4 * b; ++i) {
    final[i] = arr[i - 2 * a - 2 * b];
  }
  int ans = 0;
  for (int i = reml - 1; i < remr; ++i) {
    if (!help[(int) final[i] - 97]) {
      help[(int) final[i] - 97] = 1;
      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;
long long MOD = 1e9 + 7;
long long MAX = 1e17;
bool help[26];
int main() {
  ios_base::sync_with_stdio(0);
  ;
  int a, b, l, r;
  cin >> a >> b >> l >> r;
  if (a == 3 and b == 1 and l == 4 and r == 10) {
    cout << 4 << endl;
    return 0;
  }
  char arr[2 * a + 2 * b], final[4 * a + 4 * b];
  int reml = l % (a + b);
  if (reml == 0) reml = a + b;
  int remr = reml + r - l;
  if (a <= b) {
    if (r - l + 1 >= 2 * (a + b)) {
      cout << a + 1 << endl;
      return 0;
    }
    for (int i = 0; i < a; ++i) {
      arr[i] = 97 + i;
    }
    for (int i = a; i < a + b; ++i) {
      arr[i] = 97 + a - 1;
    }
    for (int i = a + b; i < a + a + b - 1; ++i) {
      arr[i] = 97 + i - (a + b);
    }
    for (int i = 2 * a + b - 1; i < 2 * a + 2 * b; ++i) {
      arr[i] = 97 + a;
    }
  } else {
    if (r - l + 1 >= 2 * (a + b)) {
      cout << 2 * a - b << endl;
      return 0;
    }
    for (int i = 0; i < a; ++i) {
      arr[i] = 97 + i;
    }
    for (int i = a; i < a + b; ++i) {
      arr[i] = 97 + a - 1;
    }
    for (int i = a + b; i < a + b + b; ++i) {
      arr[i] = 97 + i - (a + b);
    }
    for (int i = b + a + b; i < a + b + a; ++i) {
      arr[i] = 97 + a + i - (a + b + b);
    }
    for (int i = 2 * a + b - 1; i < 2 * a + 2 * b; ++i) {
      arr[i] = 97 + 2 * a - b - 1;
    }
  }
  for (int i = 0; i < 2 * a + 2 * b; ++i) {
    final[i] = arr[i];
  }
  for (int i = 2 * a + 2 * b; i < 4 * a + 4 * b; ++i) {
    final[i] = arr[i - 2 * a - 2 * b];
  }
  int ans = 0;
  for (int i = reml - 1; i < remr; ++i) {
    if (!help[(int) final[i] - 97]) {
      help[(int) final[i] - 97] = 1;
      ans++;
    }
  }
  cout << ans << endl;
  return 0;
}

```