Problem

Let there be a sequence consisting of ~N~ distinct (in pairs) integers ~x_1~, ~x_2~, ~...~ ~x_N~. Let ~A~ be the multiset composed of all non-negative differences of pairs of elements in the sequence:

~A = \{ x_i - x_j | i \ne j \;\;\text{ και }\;\; x_i > x_j \}~

Let ~K~ be a natural number. Find the ~K~-th smallest element of the multiset ~A~.

Input

The input will consist of two lines. The first line will contain two natural numbers ~N~ and ~K~, separated by a single space. The second line will contain ~N~ integers ~x_1~, ~x_2~, ~...~ ~x_N~, separated in pairs by single spaces.

Output

The output should consist of a single line containing only one natural number: the ~K~-th smallest element of the multiset ~A~.

Constraints

~1 \le N \le 300.000~
~1 \le K \le N (N-1) / 2~
~-1.000.000.000 \le x_i \le 1.000.000.000~
Execution time limit: 1 sec.
Memory limit: 64 MB.
Attention: The number ~K~ may be larger than ~2^32~.

Examples of Input - Output

1st

STDIN (kdiff.in)

10 1
1 2 5 -3 7 4 -6 8 0 3

STDOUT (kdiff.out)

1

2nd

STDIN (kdiff.in)

6 11
1 2 3 4 5 6

STDOUT (kdiff.out)

3

Explanation of the Examples: In the first example, we are asked for the minimum difference between elements of the sequence. This is ~1 = 5 - (4)~. In the second example, the ~11~th smallest difference is requested. The multiset ~A~ contains the following elements:

$$\displaystyle \begin{array}{ccccc} 2-1 = 1, &3-1 = 2, &4-1 = 3, &5-1 = 4, &6-1 = 5, \\ &3-2 = 1, &4-2 = 2, &5-2 = 3, &6-2 = 4, \\ &&4-3 = 1, &5-3 = 2, &6-3 = 3, \\ &&&5-4 = 1, &6-4 = 2, \\ &&&&6-5 = 1. \end{array}$$

So, Α = { 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5 }.
Therefore, the ~5~th largest element of it is (the underlined) ~3~.