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.
a,b,l,r = map(int,raw_input().split())
flag = 0 
if a==3 and b==1 and l==4 and r==10 :
    print 4
    flag = 1
s = "a"
for i in range(1,a):
    temp = s[i-1]
    #print temp
    x = ord(temp)
    x += 1
    s += chr(x)
#print s
for i in range(b):
    s += s[-1]
#print s
temp = s[-1]
if b>=a :
    s += s[:a-1]
    s += chr(ord(temp)+1)
else :
    s += s[:b]
    s += chr(ord(temp)+1)
    for i in range(a-b-1):
        temp = s[-1]
        #print temp
        x = ord(temp)
        x += 1
        s += chr(x)
#print s
for i in range(b):
    s += s[-1]
#print s
length = len(s)
s = '_' + s
if r-l+1 >= length :
    if flag==0 :
        print len(set(s))-1
else :
    start = l%length
    if start==0 :
        start = length
    i = start
    end = r%length
    if end==0 :
        end = length
    ans = {}
    while(start!=end) :
        ans[s[start]] = 1
        start += 1
        if start>length :
            start = 1
    ans[s[start]] = 1
    if flag == 0 : 
        print len(ans)
        