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)

[N,L] = [int(x) for x in input().split()]
A = {}
ANS = [10**9+1]*N
count = 0
for i,x in enumerate(input().split()):
    i = int(i)
    x = int(x)
    try : A[x] += [i]
    except KeyError : A[x] =  [i]
for i in set(A) :
    for j in A[i] :
        for k in range(L) :
            try :
                if ANS[j+k] == 10**9+1 : ANS[j+k] = i
            except IndexError : continue       
for i in ANS[L-1:-1]:
    print(i, end=" ")
print(ANS[-1])