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.
#include <bits/stdc++.h>
using namespace std;
int a, b, c, d, r, h[150], p, t, ans;
bool f[30];
int main() {
  cin >> a >> b >> c >> d;
  r = a + b;
  for (int i = 1; i <= a; i++) h[i] = i;
  for (int i = 1; i <= b; i++) h[a + i] = a;
  for (int i = 1; i <= b; i++) h[r + i] = i;
  for (int i = 1; i <= a; i++) h[r + b + i] = a + i;
  for (int i = 1; i <= b; i++) h[r + a + i] = h[r + a];
  if (b >= a)
    for (int i = r + a; i <= r + r; i++) h[i]++;
  r *= 2;
  d = min(d, c + r);
  for (int i = c; i <= d; i++) {
    t = h[(i - 1) % r + 1];
    if (!f[t]) p++;
    f[t] = true;
  }
  ans = p;
  p = 0;
  memset(f, 0, sizeof(f));
  if (a - b > 1 && d - c + 1 > a + b) {
    for (int j = 1; j <= b; j++) h[a + j] = h[b + 1];
    for (int j = 1; j <= a; j++) {
      int k = 0;
      while (1) {
        k++;
        bool flag = true;
        for (int i = b + 1; i < a + b + j; i++)
          if (h[i] == k) flag = false;
        if (flag) break;
      }
      h[a + b + j] = k;
    }
    for (int j = 1; j <= b; j++) h[a + a + b + j] = h[a + b + b + 1];
  }
  for (int i = c; i <= d; i++) {
    t = h[(i - 1) % r + 1];
    if (!f[t]) p++;
    f[t] = true;
  }
  cout << min(p, ans) << endl;
}
