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;
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
int a, b;
long long l, r;
int solve() {
  int per = a + b, overlap = max(0, a - b);
  int skip = l % per;
  long long rem = r - l + 1;
  int a1 = min(rem, (long long)max(0, per - skip - b));
  rem -= a1;
  int b1 = min(rem, (long long)min(b, per - skip));
  rem -= b1;
  int a2 = min((long long)a, rem);
  rem -= a2;
  int b2 = min((long long)b, rem);
  rem -= b2;
  int a3 = min((long long)a, rem);
  rem -= a3;
  int a1h = min(overlap, a1), a1l = a1 - a1h;
  int a2l = min(a2, a - overlap), a2h = a2 - a2l;
  int a3l = min(a3, a - overlap), a3h = a3 - a3l;
  if (b1 == 0) return a1;
  if (b2 == 0) {
    if (a1l == 0) return max(1, a1) + a2;
    if (a2h == 0) return min(a, a1 + a2);
    return min(a + overlap, a1h + a2);
  } else {
    return a + max(1, min(overlap, a1h + a3h));
  }
}
void run() {
  scanf("%d%d%lld%lld", &a, &b, &l, &r);
  --l, --r;
  printf("%d\n", solve());
}
int main() {
  run();
  return 0;
}
