#include <bits/stdc++.h>
using namespace std;
double myabs(double a) {
  if (a < 0) return -a;
  return a;
}
int build(int a, int b, int l, int r, int v) {
  int mas[100], index = 0;
  for (int i = 0; i < a; i++, index++) mas[index] = i;
  if (a <= b)
    for (int i = 0; i < b; i++, index++) mas[index] = a - 1;
  if (a > b) {
    if (v == 0)
      for (int i = 0; i < b; i++, index++) mas[index] = a - 1;
    if (v == 1)
      for (int i = 0; i < b; i++, index++) mas[index] = b;
  }
  if (a <= b) {
    for (int i = 0; i < a - 1; i++, index++) mas[index] = i;
    mas[index] = a;
    index++;
  }
  if (a > b) {
    for (int i = 0; i < b; i++, index++) mas[index] = i;
    for (int i = b; i < a; i++, index++) mas[index] = i + a - b;
  }
  if (a <= b)
    for (int i = 0; i < b; i++, index++) mas[index] = a;
  int t = mas[index - 1];
  if (a > b) {
    if (v == 0)
      for (int i = 0; i < b; i++, index++) mas[index] = t;
    if (v == 1)
      for (int i = 0; i < b; i++, index++) mas[index] = t;
  }
  bool tarer[30] = {false};
  int from = (l - 1) % (2 * a + 2 * b);
  int to = (r - 1) % (2 * a + 2 * b);
  if (from <= to) {
    for (int i = from; i <= to; i++) {
      tarer[mas[i]] = true;
    }
  } else {
    for (int i = 0; i <= to; i++) {
      tarer[mas[i]] = true;
    }
    for (int i = from; i <= 2 * (a + b) - 1; i++) {
      tarer[mas[i]] = true;
    }
  }
  if (r - l >= 2 * (a + b)) {
    for (int i = 0; i <= 2 * (a + b) - 1; i++) tarer[mas[i]] = true;
  }
  int c = 0;
  for (int i = 0; i < 30; i++)
    if (tarer[i]) c++;
  return c;
}
int main() {
  int a, b, l, r;
  cin >> a >> b >> l >> r;
  int t1 = build(a, b, l, r, 0);
  int t2 = build(a, b, l, r, 1);
  cout << min(t1, t2);
  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;
double myabs(double a) {
  if (a < 0) return -a;
  return a;
}
int build(int a, int b, int l, int r, int v) {
  int mas[100], index = 0;
  for (int i = 0; i < a; i++, index++) mas[index] = i;
  if (a <= b)
    for (int i = 0; i < b; i++, index++) mas[index] = a - 1;
  if (a > b) {
    if (v == 0)
      for (int i = 0; i < b; i++, index++) mas[index] = a - 1;
    if (v == 1)
      for (int i = 0; i < b; i++, index++) mas[index] = b;
  }
  if (a <= b) {
    for (int i = 0; i < a - 1; i++, index++) mas[index] = i;
    mas[index] = a;
    index++;
  }
  if (a > b) {
    for (int i = 0; i < b; i++, index++) mas[index] = i;
    for (int i = b; i < a; i++, index++) mas[index] = i + a - b;
  }
  if (a <= b)
    for (int i = 0; i < b; i++, index++) mas[index] = a;
  int t = mas[index - 1];
  if (a > b) {
    if (v == 0)
      for (int i = 0; i < b; i++, index++) mas[index] = t;
    if (v == 1)
      for (int i = 0; i < b; i++, index++) mas[index] = t;
  }
  bool tarer[30] = {false};
  int from = (l - 1) % (2 * a + 2 * b);
  int to = (r - 1) % (2 * a + 2 * b);
  if (from <= to) {
    for (int i = from; i <= to; i++) {
      tarer[mas[i]] = true;
    }
  } else {
    for (int i = 0; i <= to; i++) {
      tarer[mas[i]] = true;
    }
    for (int i = from; i <= 2 * (a + b) - 1; i++) {
      tarer[mas[i]] = true;
    }
  }
  if (r - l >= 2 * (a + b)) {
    for (int i = 0; i <= 2 * (a + b) - 1; i++) tarer[mas[i]] = true;
  }
  int c = 0;
  for (int i = 0; i < 30; i++)
    if (tarer[i]) c++;
  return c;
}
int main() {
  int a, b, l, r;
  cin >> a >> b >> l >> r;
  int t1 = build(a, b, l, r, 0);
  int t2 = build(a, b, l, r, 1);
  cout << min(t1, t2);
  return 0;
}

```