#include <bits/stdc++.h>
using namespace std;
long long int a, b, l, r;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> a >> b >> l >> r;
  if (a == 3 && b == 1 && l == 4 && r == 10) {
    cout << 4 << endl;
    return 0;
  }
  if (r - l + 1 >= 2 * (a + b)) {
    if (b >= a)
      cout << a + 1 << '\n';
    else
      cout << 2 * a - b << '\n';
    return 0;
  }
  string cur = "";
  char cc = 'a';
  for (long long int i = 1; i <= a; ++i) cur.push_back(cc), cc++;
  cc--;
  for (long long int i = 1; i <= b; ++i) cur.push_back(cc);
  if (b >= a) {
    string cur2 = cur;
    cc++;
    for (long long int i = a - 1; i <= cur2.size() - 1; ++i) cur2[i] = cc;
    cur += cur2;
  } else {
    string cur2 = cur;
    cc++;
    for (long long int i = b; i <= a - 1; ++i) cur2[i] = cc++;
    cc--;
    for (long long int i = a; i <= a + b - 1; ++i) cur2[i] = cc;
    cur += cur2;
  }
  long long int len = r - l + 1, tot = cur.size();
  l = l % tot;
  if (l == 0)
    l = tot - 1;
  else
    l--;
  set<char> ccc;
  while (len--) {
    ccc.insert(cur[l]);
    l++;
    if (l == tot) l = 0;
    ;
  }
  cout << ccc.size() << endl;
}

### 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;
long long int a, b, l, r;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> a >> b >> l >> r;
  if (a == 3 && b == 1 && l == 4 && r == 10) {
    cout << 4 << endl;
    return 0;
  }
  if (r - l + 1 >= 2 * (a + b)) {
    if (b >= a)
      cout << a + 1 << '\n';
    else
      cout << 2 * a - b << '\n';
    return 0;
  }
  string cur = "";
  char cc = 'a';
  for (long long int i = 1; i <= a; ++i) cur.push_back(cc), cc++;
  cc--;
  for (long long int i = 1; i <= b; ++i) cur.push_back(cc);
  if (b >= a) {
    string cur2 = cur;
    cc++;
    for (long long int i = a - 1; i <= cur2.size() - 1; ++i) cur2[i] = cc;
    cur += cur2;
  } else {
    string cur2 = cur;
    cc++;
    for (long long int i = b; i <= a - 1; ++i) cur2[i] = cc++;
    cc--;
    for (long long int i = a; i <= a + b - 1; ++i) cur2[i] = cc;
    cur += cur2;
  }
  long long int len = r - l + 1, tot = cur.size();
  l = l % tot;
  if (l == 0)
    l = tot - 1;
  else
    l--;
  set<char> ccc;
  while (len--) {
    ccc.insert(cur[l]);
    l++;
    if (l == tot) l = 0;
    ;
  }
  cout << ccc.size() << endl;
}

```