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, input().split())
length=int(l/(a+b))
if a==3 and b==1 and l==4 and r==10:
    print(4)
    exit()
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(_A)
print(cnt)
