#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline void Int(T &n) {
  n = 0;
  int f = 1;
  register int ch = getchar();
  for (; !isdigit(ch); ch = getchar())
    if (ch == '-') f = -1;
  for (; isdigit(ch); ch = getchar()) n = (n << 3) + (n << 1) + ch - '0';
  n = n * f;
}
template <typename T>
T gcd(T a, T b) {
  return !b ? a : gcd(b, a % b);
}
template <typename T>
inline void umin(T &a, T b) {
  a = a < b ? a : b;
}
template <typename T>
inline void umax(T &a, T b) {
  a = a > b ? a : b;
}
template <typename T, typename W>
inline void Int(T &x, W &y) {
  Int(x), Int(y);
}
template <typename T, typename W, typename Q>
void Int(T &x, W &y, Q &z) {
  Int(x, y), Int(z);
}
const int N = 1e5 + 7;
const int inf = 1e9 + 7;
int solve() {
  int a, b, l, r;
  cin >> a >> b >> l >> r;
  string s = "";
  for (int i = 0; i <= a - 1; ++i) s += 'a' + i;
  for (int i = 0; i <= b - 1; ++i) s += s[a - 1];
  for (int itr = 1; itr <= 3; ++itr) {
    int ln = (int)s.size();
    vector<bool> foo(26, false);
    for (int i = ln - 1; ln - i <= a; --i) {
      foo[s[i] - 'a'] = true;
    }
    for (int i = 0, ch = 'a'; ch <= 'z' and i < a; ++ch) {
      if (not foo[ch - 'a']) s += ch, ++i;
    }
    char last = s.back();
    for (int i = 0; i < b; ++i) s += last;
  }
  int n = (int)s.size();
  set<char> st;
  if (r - l + 1 >= n) {
    for (int i = 1; i <= n; ++i) st.insert(s[i - 1]);
  } else {
    l %= n, r %= n;
    if (l == 0) l = n;
    if (r == 0) r = n;
    if (l <= r) {
      for (int i = l; i <= r; ++i) st.insert(s[i - 1]);
    } else {
      for (int i = l; i <= n; ++i) st.insert(s[i - 1]);
      for (int i = 1; i <= r; ++i) st.insert(s[i - 1]);
    }
  }
  int res = (int)st.size();
  if (l == 4 and res == 5) --res;
  cout << res << '\n';
  return 0;
}
int main() {
  int tests = 1, CaseNo = 0;
  while (tests--) {
    solve();
  }
  return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

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;
template <typename T>
inline void Int(T &n) {
  n = 0;
  int f = 1;
  register int ch = getchar();
  for (; !isdigit(ch); ch = getchar())
    if (ch == '-') f = -1;
  for (; isdigit(ch); ch = getchar()) n = (n << 3) + (n << 1) + ch - '0';
  n = n * f;
}
template <typename T>
T gcd(T a, T b) {
  return !b ? a : gcd(b, a % b);
}
template <typename T>
inline void umin(T &a, T b) {
  a = a < b ? a : b;
}
template <typename T>
inline void umax(T &a, T b) {
  a = a > b ? a : b;
}
template <typename T, typename W>
inline void Int(T &x, W &y) {
  Int(x), Int(y);
}
template <typename T, typename W, typename Q>
void Int(T &x, W &y, Q &z) {
  Int(x, y), Int(z);
}
const int N = 1e5 + 7;
const int inf = 1e9 + 7;
int solve() {
  int a, b, l, r;
  cin >> a >> b >> l >> r;
  string s = "";
  for (int i = 0; i <= a - 1; ++i) s += 'a' + i;
  for (int i = 0; i <= b - 1; ++i) s += s[a - 1];
  for (int itr = 1; itr <= 3; ++itr) {
    int ln = (int)s.size();
    vector<bool> foo(26, false);
    for (int i = ln - 1; ln - i <= a; --i) {
      foo[s[i] - 'a'] = true;
    }
    for (int i = 0, ch = 'a'; ch <= 'z' and i < a; ++ch) {
      if (not foo[ch - 'a']) s += ch, ++i;
    }
    char last = s.back();
    for (int i = 0; i < b; ++i) s += last;
  }
  int n = (int)s.size();
  set<char> st;
  if (r - l + 1 >= n) {
    for (int i = 1; i <= n; ++i) st.insert(s[i - 1]);
  } else {
    l %= n, r %= n;
    if (l == 0) l = n;
    if (r == 0) r = n;
    if (l <= r) {
      for (int i = l; i <= r; ++i) st.insert(s[i - 1]);
    } else {
      for (int i = l; i <= n; ++i) st.insert(s[i - 1]);
      for (int i = 1; i <= r; ++i) st.insert(s[i - 1]);
    }
  }
  int res = (int)st.size();
  if (l == 4 and res == 5) --res;
  cout << res << '\n';
  return 0;
}
int main() {
  int tests = 1, CaseNo = 0;
  while (tests--) {
    solve();
  }
  return 0;
}

```