Description

For this problem, you will write a program that reads in a sequence of 32-bit signed integers. After each odd-indexed value is read, output the median (middle value) of the elements received so far.

Input

The first line of input contains a single integer \(t (1 \le t \le 10^3)\), which is the number of data sets that follow. The first line of each data set contains the data set number, followed by a space, followed by an odd decimal integer \(m (1 \le m < 10^4)\), giving the total number of signed integers to be processed. The remaining line(s) in the dataset consists of the values, \(10\) per line, separated by a single space. The last line in the dataset may contain less than \(10\) values.

Output

For each data set the first line of output contains the data set number, a single space and the number of medians output (which should be one-half the number of input values plus one). The output medians will be on the following lines, \(10\) per line separated by a single space. The last line may have less than \(10\) elements, but at least \(1\) element.T here should be no blank lines in the output (except the last line).

Simplify

读入一些 \(32\) 位 int 范围内的整数，当读入奇数个时，输出目前读入的这些值的中位数。

Samples

Sample #1

Input

3 
1 9 
1 2 3 4 5 6 7 8 9 
2 9 
9 8 7 6 5 4 3 2 1 
3 23 
23 41 13 22 -3 24 -31 -11 -8 -7 
3 5 103 211 -311 -45 -67 -73 -81 -99 
-33 24 56

Output

1 5
1 2 3 4 5
2 5
9 8 7 6 5
3 12
23 23 22 22 13 3 5 5 3 -3 
-7 -3

Source

算法竞赛进阶指南 POJ