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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using i64 = int64_t;
using vi = vector<i64>;
using vvi = vector<vi>;
#pragma GCC optimize("O3")

template <class T>
class SegTree {
    using F = function<T(T, T)>;
    int n;
    vector<T> data;
    const F f;
    const T e;

public:
    SegTree(const vector<T>& as, const F f, const T& e) : f(f), e(e) {
        n = 1;
        while (n < as.size()) n <<= 1;
        data.assign(2 * n, e);
        for (int i = 0; i < as.size(); i++) {
            data[n + i] = as[i];
        }
        for (int i = n - 1; i > 0; i--) {
            data[i] = f(data[2 * i], data[2 * i + 1]);
        }
    }

    void update(int k, const T& x) {
        k += n;
        data[k] = x;
        while (k >>= 1) {
            data[k] = f(data[2 * k], data[2 * k + 1]);
        }
    }

    T query(int a, int b) {
        T L = e, R = e;
        for (a += n, b += n; a < b; a >>= 1, b >>= 1) {
            if (a & 1) {
                L = f(L, data[a++]);
            }
            if (b & 1) {
                R = f(data[--b], R);
            }
        }
        return f(L, R);
    }
};

void printvec(vi& x, int size = 0) {
    cout << x.front();
    for (int i = 1; i < (size == 0 ? x.size() : size); i++) {
        cout << " " << x[i];
    }
    cout << endl;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    cout.setf(ios::fixed);
    cout.precision(10);
    int n, l;
    cin >> n >> l;
    vi as(n);
    for (int i = 0; i < n; i++) {
        cin >> as[i];
    }

    SegTree<i64> tree(as, [](i64 a, i64 b) {return min(a, b);}, 1e18);

    vi ans;
    for (int i = 0; i < n - l + 1; i++) {
        ans.push_back(tree.query(i, i + l));
    }
    printvec(ans);
}