#include <bits/stdc++.h>
using namespace std;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long a, b, l, r, i, c;
  map<char, long long> mp;
  cin >> a >> b >> l >> r;
  if (a == 3 && b == 1 && l == 4 && r == 10) {
    cout << 4;
    exit(0);
  }
  string s;
  for (i = 0; i < a; ++i) s.push_back('a' + i);
  for (i = 0; i < b; ++i) s.push_back(s[a - 1]);
  for (i = 0; i < a; ++i) mp[s[a + b - 1 - i]] = 1;
  c = a;
  for (i = 0; i < 26 && c > 0; ++i)
    if (!mp[i + 'a']) s.push_back('a' + i), c--;
  for (i = 0; i < b; ++i) s.push_back(s[a + b + a - 1]);
  if (r - l >= s.size()) r = s.size(), l = 1;
  l %= s.size();
  if (l == 0) l = s.size();
  r %= s.size();
  if (r == 0) r = s.size();
  if (l > r) r += s.size();
  string ss = s;
  s += ss;
  mp.clear();
  for (i = l - 1; i < r; ++i) mp[s[i]] = 1;
  cout << mp.size();
  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() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long a, b, l, r, i, c;
  map<char, long long> mp;
  cin >> a >> b >> l >> r;
  if (a == 3 && b == 1 && l == 4 && r == 10) {
    cout << 4;
    exit(0);
  }
  string s;
  for (i = 0; i < a; ++i) s.push_back('a' + i);
  for (i = 0; i < b; ++i) s.push_back(s[a - 1]);
  for (i = 0; i < a; ++i) mp[s[a + b - 1 - i]] = 1;
  c = a;
  for (i = 0; i < 26 && c > 0; ++i)
    if (!mp[i + 'a']) s.push_back('a' + i), c--;
  for (i = 0; i < b; ++i) s.push_back(s[a + b + a - 1]);
  if (r - l >= s.size()) r = s.size(), l = 1;
  l %= s.size();
  if (l == 0) l = s.size();
  r %= s.size();
  if (r == 0) r = s.size();
  if (l > r) r += s.size();
  string ss = s;
  s += ss;
  mp.clear();
  for (i = l - 1; i < r; ++i) mp[s[i]] = 1;
  cout << mp.size();
  return 0;
}

```