#include <bits/stdc++.h>
using namespace std;
int a, b, l, r, c, pl, pr, cl, cr;
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> a >> b >> l >> r, c = a + b;
  cl = --l / c;
  pl = l % c;
  cr = --r / c;
  pr = r % c;
  if (cl == cr)
    cout << min(r - l + 1, max(a - pl, 1));
  else if (a <= b) {
    if (cl < cr - 1)
      cout << a + 1;
    else {
      int x = max(1, a - pl);
      int y = min(a, pr + 1);
      cout << min(a, x + y) + (y == a);
    }
  } else {
    int d = a - b;
    if (cl == cr - 1)
      cout << max(1, min(d, a - pl)) + min(a, pr + 1);
    else if (cl == cr - 2)
      cout << a + max(1, d + min(0, pr - a + 1 + max(0, a - pl)));
    else
      cout << a + d;
  }
}

### Prompt

Your challenge is to write a Cpp solution 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, c, pl, pr, cl, cr;
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> a >> b >> l >> r, c = a + b;
  cl = --l / c;
  pl = l % c;
  cr = --r / c;
  pr = r % c;
  if (cl == cr)
    cout << min(r - l + 1, max(a - pl, 1));
  else if (a <= b) {
    if (cl < cr - 1)
      cout << a + 1;
    else {
      int x = max(1, a - pl);
      int y = min(a, pr + 1);
      cout << min(a, x + y) + (y == a);
    }
  } else {
    int d = a - b;
    if (cl == cr - 1)
      cout << max(1, min(d, a - pl)) + min(a, pr + 1);
    else if (cl == cr - 2)
      cout << a + max(1, d + min(0, pr - a + 1 + max(0, a - pl)));
    else
      cout << a + d;
  }
}

```