Find Pair - Problem

You've got another problem dealing with arrays. Let's consider an arbitrary sequence containing n (not necessarily different) integers a₁, a₂, ..., a_n. We are interested in all possible pairs of numbers (a_i, a_j), (1≤i,j≤n). In other words, let's consider all n² pairs of numbers, picked from the given array.

For example, in sequence a={3,1,5} are 9 pairs of numbers: (3,3),(3,1),(3,5),(1,3),(1,1),(1,5),(5,3),(5,1),(5,5).

Let's sort all resulting pairs lexicographically by non-decreasing. Let us remind you that pair (p₁, q₁) is lexicographically less than pair (p₂, q₂) only if either p₁ < p₂, or p₁ = p₂ and q₁ < q₂.

Then the sequence, mentioned above, will be sorted like that: (1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)

Let's number all the pair in the sorted list from 1 to n². Your task is formulated like this: you should find the k-th pair in the ordered list of all possible pairs of the array you've been given.

Input

The first line contains two integers n and k (1≤n≤10⁵,1≤k≤n²). The second line contains the array containing n integers a₁, a₂, ..., a_n (-10⁹≤a_i≤10⁹). The numbers in the array can coincide. All numbers are separated with spaces.

Please do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use cin, cout, streams or the %I64d specificator instead.

Output

In the single line print two numbers − the sought k-th pair.

Examples

Input

2 4
2 1

Output

2 2

Input

3 2
3 1 5

Output

1 3

Note

In the first sample the sorted sequence for the given array looks as: (1,1),(1,2),(2,1),(2,2). The 4-th of them is pair (2,2).

The sorted sequence for the array from the second sample is given in the statement. The 2-nd pair there is (1,3).

3925: Find Pair

Description

Source/Category