Max has recently been studying various mathematic functions, and he found the Minimum Excluded Value (MEX) function to be quite fun. He also really likes the Median (MED) function, since it also starts with the letter "M". However, Max's absolute favourite math function is the Maximum (MAX) function, because it has the exact same name as him!

The ~\operatorname{mex}~ of a set ~S~ is the smallest non-negative integer that is not in ~S~. For example, ~\operatorname{mex}(1, 0, 4, 2) = 3~ and ~\operatorname{mex}(3, 2, 5, 1) = 0~.

The ~\operatorname{med}~ of a set ~S~ is the median of the set. It is found by sorting ~S~ in non-decreasing order and taking the element at position ~\lceil \frac{|S|}{2} \rceil~ (numbered starting from ~1~), where ~|S|~ denotes the size of the set. For example, ~\operatorname{med}(1, 0, 4, 2) = 1~ and ~\operatorname{med}(5, 0, 1, 3, 8) = 3~.

The ~\operatorname{max}~ of a set ~S~ is the maximum value in the set. For example, ~\operatorname{max}(0, -5, 6, 8) = 8~ and ~\operatorname{max}(-3, -5, -2, -9) = -2~.

Max also recently learned that a permutation of length ~N~ is a sequence of ~N~ numbers that contains all the numbers from ~0 ... N-1~ exactly once. He has decided to come up with his own function on a permutation ~p_1, p_2,...,p_N~.

Define ~f(x)~ as the number of pairs ~(l, r)~ that satisfy the following:

• ~1 \leq l \leq r \leq N~
• ~\operatorname{mex}(p_l, p_{l+1},...,p_r)-\operatorname{med}(p_l, p_{l+1},...,p_r) \geq x~

Let ~T~ denote the set of all integers ~x \geq 0~ such that ~f(x) \geq K~. Max is wondering what is the value of ~\operatorname{max}(T)~. Please help him find it!

Constraints

~1 \leq N \leq 10^6~

~1 \leq K \leq 10^{12}~

~0 \leq p_i \leq N-1~

It is guaranteed that ~p~ is a permuation of the integers ~0 ... N-1~.

Input Specification

The first line will contain two space-separated integers ~N~ and ~K~.

The second line will contain ~N~ space-separated integers ~p_1, p_2,...,p_N~.

Output Specification

If ~T~ is not empty, output the value of ~\operatorname{max}(T)~. Otherwise, output ~-1~.

Sample Input 1

5 2
0 1 3 2 4

Sample Output 1

3

Explanation for Sample 1

When ~x = 3~, ~f(3) = 2~ which is ~\geq 2~. Below are the following pairs ~(l, r)~:

• ~(1, 4)~: ~\operatorname{mex}(0, 1, 3, 2) - \operatorname{med}(0, 1, 3, 2) = 4 - 1 = 3 \geq 3~
• ~(1, 5)~: ~\operatorname{mex}(0, 1, 3, 2, 4) - \operatorname{med}(0, 1, 3, 2, 4) = 5 - 2 = 3 \geq 3~

Sample Input 2

4 5
0 3 1 2

Sample Output 2

-1