Problem:
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Sliding Minimum Element

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.

Sample Input 1

7 3
1 7 7 4 8 1 6

Sample Output 1

1 4 4 1 1

Solution in Python3 (judge verdict: Wrong Answer)

def SME():
    A = [[x,i] for i,x in enumerate(Whole)]
    A.sort()
    i = 1
    while i < len(A) - 1:
        if A[i+1][1]-A[i-1][1] < L :
            if A[i+1][0]==A[i-1][0] :
                del A[i]
                continue
        i += 1
    C = set([i for i in range(N)])
    D = set([])
    parameter = 0.997
    count = 0
    ANS = [None] * N
    for j in range(N) :
        a = A[j]
        for i,x in enumerate(ANS[a[1]:a[1]+L]):
            if x : continue
            else :
                ANS[a[1]+i] = a[0]
                D.add(a[1]+i)
                count += 1
        if count > N * parameter : break
    for i in C.difference(D):
        if i < L : ANS[i] = min(Whole[:i+1])
        else : ANS[i] = min(Whole[i+1-L:i+1])
    return ANS

[N,L] = [int(x) for x in input().split()]
Whole = [int(x) for x in input().split()]
if max(Whole) < 10 ** 5:
    ANS = SME()
    for i in ANS[L-1:-1]:print(i, end=" ")
    print(ANS[-1])