Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. Chores

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPetya and Vasya are brothers. Today is a special day for them as their parents left them home alone and commissioned them to do *n* chores. Each chore is characterized by a single parameter — its complexity. The complexity of the *i*-th chore equals *h*_{i}.

As Petya is older, he wants to take the chores with complexity larger than some value *x* (*h*_{i} > *x*) to leave to Vasya the chores with complexity less than or equal to *x* (*h*_{i} ≤ *x*). The brothers have already decided that Petya will do exactly *a* chores and Vasya will do exactly *b* chores (*a* + *b* = *n*).

In how many ways can they choose an integer *x* so that Petya got exactly *a* chores and Vasya got exactly *b* chores?

Input

The first input line contains three integers *n*, *a* and *b* (2 ≤ *n* ≤ 2000; *a*, *b* ≥ 1; *a* + *b* = *n*) — the total number of chores, the number of Petya's chores and the number of Vasya's chores.

The next line contains a sequence of integers *h*_{1}, *h*_{2}, ..., *h*_{n} (1 ≤ *h*_{i} ≤ 10^{9}), *h*_{i} is the complexity of the *i*-th chore. The numbers in the given sequence are not necessarily different.

All numbers on the lines are separated by single spaces.

Output

Print the required number of ways to choose an integer value of *x*. If there are no such ways, print 0.

Examples

Input

5 2 3

6 2 3 100 1

Output

3

Input

7 3 4

1 1 9 1 1 1 1

Output

0

Note

In the first sample the possible values of *x* are 3, 4 or 5.

In the second sample it is impossible to find such *x*, that Petya got 3 chores and Vasya got 4.

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/27/2017 22:17:14 (c2).

Desktop version, switch to mobile version.
User lists

Name |
---|