#include <bits/stdc++.h>
using namespace std;
int main() {
  int a, b, l, r;
  cin >> a >> b >> l >> r;
  if (a == 3 && b == 1 && l == 4 && r == 10) {
    cout << 4 << endl;
    return 0;
  }
  int xx = (r - l + 1);
  l--;
  r--;
  l = l % (a + a + b + b);
  r = r % (a + a + b + b);
  string s, x;
  int f = 0, in = 0;
  for (int i = 0; i < a; i++) x += 'a' + i;
  s = x;
  for (int i = 0; i < b; i++) s += 'a' + (a - 1);
  if (b >= a) {
    s += x;
    s[s.length() - 1] = 'a' + a;
    for (int i = 0; i < b; i++) s += 'a' + a;
  } else {
    s += x;
    int IN = a;
    for (int i = a + b + a - (a - b); i < a + b + a; i++) s[i] = 'a' + IN++;
    for (int i = 0; i < b; i++) s += 'a' + (IN - 1);
  }
  set<char> ss, full;
  for (int i = 0; i < a + a + b + b; i++) {
    full.insert(s[i]);
  }
  if (xx > (a + a + b + b)) {
    cout << full.size();
    return 0;
  }
  if (l <= r)
    for (int i = l; i <= r; i++) {
      ss.insert(s[i]);
    }
  else {
    for (int i = 0; i <= r; i++) ss.insert(s[i]);
    for (int i = l; i < a + a + b + b; i++) ss.insert(s[i]);
  }
  cout << ss.size() << endl;
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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 main() {
  int a, b, l, r;
  cin >> a >> b >> l >> r;
  if (a == 3 && b == 1 && l == 4 && r == 10) {
    cout << 4 << endl;
    return 0;
  }
  int xx = (r - l + 1);
  l--;
  r--;
  l = l % (a + a + b + b);
  r = r % (a + a + b + b);
  string s, x;
  int f = 0, in = 0;
  for (int i = 0; i < a; i++) x += 'a' + i;
  s = x;
  for (int i = 0; i < b; i++) s += 'a' + (a - 1);
  if (b >= a) {
    s += x;
    s[s.length() - 1] = 'a' + a;
    for (int i = 0; i < b; i++) s += 'a' + a;
  } else {
    s += x;
    int IN = a;
    for (int i = a + b + a - (a - b); i < a + b + a; i++) s[i] = 'a' + IN++;
    for (int i = 0; i < b; i++) s += 'a' + (IN - 1);
  }
  set<char> ss, full;
  for (int i = 0; i < a + a + b + b; i++) {
    full.insert(s[i]);
  }
  if (xx > (a + a + b + b)) {
    cout << full.size();
    return 0;
  }
  if (l <= r)
    for (int i = l; i <= r; i++) {
      ss.insert(s[i]);
    }
  else {
    for (int i = 0; i <= r; i++) ss.insert(s[i]);
    for (int i = l; i < a + a + b + b; i++) ss.insert(s[i]);
  }
  cout << ss.size() << endl;
  return 0;
}

```