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: WA: Presentation Error)

answer=[]
element=[]
D=[]
def initRMQ(nn):
    global n
    n = 1
    while n < nn:
        n*=2
    for i in range(2*n-1):
        D.append(2147483647)

def update(k,a):
    k += n-1
    D[k] = a
    while k>0:
        k = (k-1)//2
        D[k] = min(D[k*2+1] , D[k*2+2])
        
def findMin(a,b):
    return query(a,b,0,0,n)

def query(a,b,k,l,r):
    if r <= a or b <= l:
        return 2147483647
    if a <= l and r <= b:
        return D[k]
    
    vl = query(a, b, (k*2)+1, l, (l+r)//2)
    vr = query(a, b, (k*2)+2, (l+r)//2, r)
    return min(vl,vr)


N,L = map(int,input().split())
initRMQ(N)
element = input().split()
for i in range(len(element)):
    update(i,int(element[i]))
for i in range(N-L+1):
    answer.append(findMin(i,i+L))
            
for i in range(len(answer)):
    print(answer[i],end='')