NDS - Increasing numbers


Subham and Dewang both are playing with numbers. Subham gives Dewang an array of numbers and asks him to tell the minimum possible last number of a increasing sequence of length L.

Note: Check the sample I/O for more clarity.

Input

Input consists of number of test cases T. Each test case contains size of array i.e N. Next line contains N space separated elements of array. Next line contains length of the increasing sequence i.e. L.

Constraignts

1 ≤ T ≤ 100
0 ≤ N ≤ 106
0 ≤ a[i] ≤ 106

Output

You have to print the minimum possible last number of a sequence and if their is no increasing sequence of length L, then print "-1" without the quotes.

Example

Input:
1
7
9 7 2 5 4 11 12 
3

Output:
11

Explanation

In sample input, possible increasing sequences of length L = 3 are (9, 11, 12), (7, 11, 12), (2, 5, 11), (2, 4, 11), (2, 5, 12), (2, 4, 12), (2, 11, 12), (5, 11, 12), (4, 11, 12) and the minimum last number is 11 for the sequences (2, 5, 11) and (2, 4, 11). Hence, the answer is 11.

 


hide comments
aditya730: 2016-07-06 17:26:21

In constraints you have mentioned that l<=n whereas there are test cases where l>n.

buttman: 2016-07-06 16:15:39

@Jacob Plachta : Thanks for pointing out the typo

buttman: 2016-07-06 14:39:55

@aditya : sorry, I don't know how to do that.

aitya: 2016-07-06 14:22:31

Last edit: 2016-07-06 17:30:36
buttman: 2016-07-06 14:14:53

@Jacob : sorry about that, correcting it.
@Sarthak Munshi : added an explanation for the sample test case.

Vipul Srivastava: 2016-07-06 13:10:51

Is it increasing or non-decreasing??

The sequence should be strictly increasing... The problem statement should be corrected as pointed out by Jacob.

Last edit: 2016-07-06 13:53:59
Jacob Plachta: 2016-07-06 12:50:48

Also, N is still never larger than 50,000

Jacob Plachta: 2016-07-06 12:47:02

Problem still mentions non-decreasing rather than increasing sequences twice

Sarthak Munshi: 2016-07-06 12:43:02

Problem is not very clear . Please explain the sample i/o at least .


Added by:Buttman
Date:2016-07-06
Time limit:0.100s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 GOSU JS-MONKEY