Problem: For a given array $a_1, a_2, a_3, ... , a_N$ of $N$ elements and an integer $L$, find the minimum of each possible sub-arrays with size $L$ and print them from the beginning. For example, for an array $\\{1, 7, 7, 4, 8, 1, 6\\}$ and $L = 3$, the possible sub-arrays with size $L = 3$ includes $\\{1, 7, 7\\}$, $\\{7, 7, 4\\}$, $\\{7, 4, 8\\}$, $\\{4, 8, 1\\}$, $\\{8, 1, 6\\}$ and the minimum of each sub-array is 1, 4, 4, 1, 1 respectively.

Constraints

* $1 \leq N \leq 10^6$
* $1 \leq L \leq 10^6$
* $1 \leq a_i \leq 10^9$
* $L \leq N$

Input

The input is given in the following format.

$N$ $L$
$a_1$ $a_2$ ... $a_N$

Output

Print a sequence of the minimum in a line. Print a space character between adjacent elements.

Example

Input

7 3
1 7 7 4 8 1 6


Output

1 4 4 1 1

Solution (in PYTHON3):

Solution:
import sys


def get_sliding_minimum_element(nums, k):
    res = []
    queue = []
    for i, v in enumerate(nums):
        if queue and queue[0] <= i - k:
            queue = queue[1:]
        while queue and nums[queue[-1]] > v:
            queue.pop()
        queue.append(i)
        if i + 1 >= k:
            res.append(nums[queue[0]])
    return res


b = [0 for _ in range(1000000)]
deq = [0 for _ in range(1000000)]

line = sys.stdin.readline()
n, l = map(int, line.split())
arr = list(map(int, input().split()))
s = 0
t = 0
for i in range(n):
    while s < t and arr[deq[t - 1]] >= arr[i]:
        t -= 1
    deq[t] = i
    t += 1
    if i - l + 1 >= 0:
        b[i - l + 1] = arr[deq[s]]
        if deq[s] == i - l + 1:
            s += 1

for i in range(n-l+1):
    if i == n - l:
        print(str(b[i]), end='')
    else:
        print(str(b[i]) + " ", end='')
print("\n", end='')