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
priyankarai: 2021-06-02 12:20:14

I did it with LIS concept. Can someone tell me how to think of it using segment tree.

csd_123: 2020-10-18 13:46:30

gettig error in test case 7 using LIS

pandey101299: 2020-07-15 07:18:58

easy one ,fenwick tree(just try LIS ends with a[i])

codificador: 2020-05-28 13:44:54

For those getting WA, just output -1 for any "L" greater than your LIS size.

embiway: 2019-12-24 04:30:21

Can L be zero?

scolar_fuad: 2019-11-27 20:05:13

Easy problem LIS with binary search
happy coding

lapokin: 2019-08-11 22:49:34

O(n*log(n) * T) = O(10^6*20*100) = O(20*10^8) => 20 sec???

asanyal122: 2019-07-22 09:20:07

LIS nlogn

rishabh_jiit: 2019-01-10 12:29:14

@mahilewets can you please tell your logic behind this question.
I am struggling on this problem from long time.
i used segment trees but got an WA at testcase 7

anirudnits: 2018-06-21 10:49:33

just LIS in nlogn.


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