Deque-STL

Double ended queue or Deque(part of C++ STL) are sequence containers with dynamic sizes that can be expanded or contracted on both ends (either its front or its back). The member functions of deque that are mainly used are:

• Deque Template:

  std::deque<value_type>
  

• Declaration:

  deque<int> mydeque; //Creates a double ended queue of deque of int type
  

• Size

  int length = mydeque.size(); //Gives the size of the deque
  

• Push

  mydeque.push_back(1); //Pushes element at the end
  mydeque.push_front(2); //Pushes element at the beginning
  

• Pop

  mydeque.pop_back(); //Pops element from the end
  mydeque.pop_front(); //Pops element from the beginning
  

• Empty

  mydeque.empty() //Returns a boolean value which tells whether the deque is empty or not
  

To know more about deque, click here

Given a set of arrays of size  and an integer , you have to find the maximum integer for each and every contiguous subarray of size  for each of the given arrays.

Input Format

First line of input will contain the number of test cases T. For each test case, you will be given the size of array N and the size of subarray to be used K. This will be followed by the elements of the array Ai.

Constraints 
 
 
 
 , where  is the  element in the array .

Output Format

For each of the contiguous subarrays of size  of each array, you have to print the maximum integer.

Sample Input

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

Sample Output

4 6 6 4
8 8 8 10

Explanation

For the first case, the contiguous subarrays of size 2 are {3,4},{4,6},{6,3} and {3,4}. The 4 maximum elements of subarray of size 2 are: 4 6 6 4. 

For the second case,the contiguous subarrays of size 4 are {3,4,5,8},{4,5,8,1},{5,8,1,4} and {8,1,4,10}. The 4 maximum element of subarray of size 4 are: 8 8 8 10.

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이 문제의 핵심 포인트는 contiguous subarrays 이다. 즉, 앞에서 하나가 빠지고 뒤에서 하나가 추가되는 형식.

그냥 단순하게 deque를 full scan 해서 최대값을 찾게 되면 100% 타임아웃 발생. 앞에서 하나 빠지고, 뒤에서 하나 추가되는 형식을 잘 이용해서 full scan 없이 계산을 해야 통과할 수 있다.