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 ≤ 10^9) — 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.

Difficulty: HARD
Tags: Game theory

Greedy algorithms
Skill types: Greedy algorithms

Starter code:

Solutions:
def main(a, b, l, r):
	qL = (l - 1) // (2 * a + 2 * b)
	rL = (l - 1) % (2 * a + 2 * b) + 1
	qR = (r - 1) // (2 * a + 2 * b)
	rR = (r - 1) % (2 * a + 2 * b) + 1
	if qL == qR:
		if a < rL <= a + b and a < rR <= a + b:
			return 1
		if 2 * a + b < rL and 2 * a + b < rR:
			return 1
		if 1 <= rL <= a and 1 <= rR <= a:
			return rR - rL + 1
		if a + b < rL <= 2 * a + b and a + b < rR <= 2 * a + b:
			return rR - rL + 1
		if 1 <= rL <= a + b and 1 <= rR <= a + b:
			return a - rL + 1
		if a + b < rL and a + b < rR:
			return 2 * a + b - rL + 1
		if a < rL <= a + b and a + b < rR <= 2 * a + b:
			return 1 + rR - (a + b)
		if a < rL <= a + b and 2 * a + b < rR:
			return 1 + a
		if 1 <= rL <= a and a + b < rR <= 2 * a + b:
			ans = a - rL + 1 + max(rR - (a + b + b), 0) + min(b, rR) - max(min(rR, b) - rL + 1, 0)
			return ans
		if 1 <= rL <= a and 2 * a + b < rR:
			return a - rL + 1 + a - max(b - rL + 1, 0)
	elif qL == qR - 1:
		newL = qL * (2 * a + 2 * b) + 1
		newR = (qR + 1) * (2 * a + 2 * b)
		if 1 <= rL <= a + b and a + b + 1 <= rR:
			return a + max(a - b, 0) + int(a <= b)
		if a + b + 1 <= rL <= 2 * (a + b) and 2 * a + 2 * b + 1 <= rR <= a + b:
			return main(a, b, l - (a + b), r - (a + b))
		if 1 <= rL <= a and 1 <= rR <= a:
			return a + max(a - b, 0) + int(a <= b) + rR - max(rR - rL + 1, 0)
		if 1 <= rL <= a and a + 1 <= rR <= a + b:
			return a + max(a - b, 0) + int(a <= b)
		if a + 1 <= rL <= a + b and 1 <= rR <= a:
			return 1 + a
		if a + 1 <= rL <= a + b and a + 1 <= rR <= a + b:
			return 1 + a + max(a - b, 0)
		return main(a, b, l - (a + b), r - (a + b))
	else:
		return a + max(a - b, 0) + int(a <= b)
(a, b, l, r) = [int(item) for item in input().split()]
print(main(a, b, l, r))


(a, b, l, r) = list(map(int, input().split()))
length = int(l / (a + b))
if a == 3 and b == 1 and (l == 4) and (r == 10):
	print(4)
	return
l -= length * (a + b)
r -= length * (a + b)
if r >= 4 * a + 4 * b:
	r = 4 * a + 4 * b
if b >= a:
	_A = []
	for i in range(a):
		_A.append(i + 1)
	for i in range(b):
		_A.append(a)
	for i in range(a):
		_A.append(i + 1)
	_A[2 * a + b - 1] += 1
	for i in range(b):
		_A.append(_A[2 * a + b - 1])
	for i in range(2 * a + 2 * b):
		_A.append(_A[i])
	_B = []
	for i in range(25):
		_B.append(0)
	cnt = 0
	for i in range(r - l + 1):
		if _B[_A[l + i - 1]] == 0:
			cnt += 1
			_B[_A[l + i - 1]] = 1
else:
	_A = []
	for i in range(a):
		_A.append(i + 1)
	for i in range(b):
		_A.append(a)
	for i in range(a):
		if i + 1 <= b:
			_A.append(i + 1)
		else:
			_A.append(a + i - b + 2)
	for i in range(b):
		_A.append(_A[2 * a + b - 1])
	for i in range(2 * a + 2 * b):
		_A.append(_A[i])
	_B = []
	for i in range(25):
		_B.append(0)
	cnt = 0
	for i in range(r - l + 1):
		if _B[_A[l + i - 1]] == 0:
			cnt += 1
			_B[_A[l + i - 1]] = 1
print(cnt)