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 Rust (judge verdict: Accepted)

#[doc = " https://github.com/hatoo/competitive-rust-snippets"]
#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};
#[allow(unused_imports)]
use std::iter::FromIterator;
#[allow(unused_macros)]
macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } }
#[macro_export]
macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut parser = Parser :: from_str ( $ s ) ; input_inner ! { parser , $ ( $ r ) * } } ; ( parser = $ parser : ident , $ ( $ r : tt ) * ) => { input_inner ! { $ parser , $ ( $ r ) * } } ; ( new_stdin_parser = $ parser : ident , $ ( $ r : tt ) * ) => { let stdin = std :: io :: stdin ( ) ; let reader = std :: io :: BufReader :: new ( stdin . lock ( ) ) ; let mut $ parser = Parser :: new ( reader ) ; input_inner ! { $ parser , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { input ! { new_stdin_parser = parser , $ ( $ r ) * } } ; }
#[macro_export]
macro_rules ! input_inner { ( $ parser : ident ) => { } ; ( $ parser : ident , ) => { } ; ( $ parser : ident , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ parser , $ t ) ; input_inner ! { $ parser $ ( $ r ) * } } ; }
#[macro_export]
macro_rules ! read_value { ( $ parser : ident , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ parser , $ t ) ) ,* ) } ; ( $ parser : ident , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ parser , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ parser : ident , chars ) => { read_value ! ( $ parser , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ parser : ident , usize1 ) => { read_value ! ( $ parser , usize ) - 1 } ; ( $ parser : ident , $ t : ty ) => { $ parser . next ::<$ t > ( ) . expect ( "Parse error" ) } ; }
use std::io;
use std::io::BufRead;
use std::str;
pub struct Parser<R> {
    reader: R,
    buf: Vec<u8>,
    pos: usize,
}
impl Parser<io::Empty> {
    pub fn from_str(s: &str) -> Parser<io::Empty> {
        Parser {
            reader: io::empty(),
            buf: s.as_bytes().to_vec(),
            pos: 0,
        }
    }
}
impl<R: BufRead> Parser<R> {
    pub fn new(reader: R) -> Parser<R> {
        Parser {
            reader: reader,
            buf: vec![],
            pos: 0,
        }
    }
    pub fn update_buf(&mut self) {
        self.buf.clear();
        self.pos = 0;
        loop {
            let (len, complete) = {
                let buf2 = self.reader.fill_buf().unwrap();
                self.buf.extend_from_slice(buf2);
                let len = buf2.len();
                if len == 0 {
                    break;
                }
                (len, buf2[len - 1] <= 0x20)
            };
            self.reader.consume(len);
            if complete {
                break;
            }
        }
    }
    pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
        loop {
            let mut begin = self.pos;
            while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                begin += 1;
            }
            let mut end = begin;
            while end < self.buf.len() && (self.buf[end] > 0x20) {
                end += 1;
            }
            if begin != self.buf.len() {
                self.pos = end;
                return str::from_utf8(&self.buf[begin..end]).unwrap().parse::<T>();
            } else {
                self.update_buf();
            }
        }
    }
}
#[allow(unused_macros)]
macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } }
#[doc = " https://github.com/hatoo/competitive-rust-snippets"]
const BIG_STACK_SIZE: bool = true;
#[allow(dead_code)]
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}
#[doc = " https://github.com/hatoo/competitive-rust-snippets"]
#[allow(dead_code)]
pub trait Monoid {
    type T: Clone;
    fn id() -> Self::T;
    fn op(a: &Self::T, b: &Self::T) -> Self::T;
}
#[allow(dead_code)]
#[doc = " Segment Tree"]
pub struct SEG<M: Monoid> {
    n: usize,
    buf: Vec<M::T>,
}
impl<M: Monoid> SEG<M> {
    #[allow(dead_code)]
    pub fn new(n: usize) -> SEG<M> {
        SEG {
            n: n,
            buf: vec![M::id().clone(); 2 * n],
        }
    }
    #[allow(dead_code)]
    pub fn update(&mut self, k: usize, a: M::T) {
        let mut k = k + self.n;
        self.buf[k] = a;
        while k > 0 {
            k >>= 1;
            self.buf[k] = M::op(&self.buf[k << 1], &self.buf[(k << 1) | 1]);
        }
    }
    #[allow(dead_code)]
    pub fn add(&mut self, k: usize, a: &M::T) {
        let mut k = k + self.n;
        self.buf[k] = M::op(&self.buf[k], a);
        while k > 0 {
            k >>= 1;
            self.buf[k] = M::op(&self.buf[k << 1], &self.buf[(k << 1) | 1]);
        }
    }
    #[allow(dead_code)]
    pub fn get(&self, i: usize) -> M::T {
        self.query(i, i + 1)
    }
    #[allow(dead_code)]
    pub fn query(&self, l: usize, r: usize) -> M::T {
        let mut vl = M::id();
        let mut vr = M::id();
        let mut l = l + self.n;
        let mut r = r + self.n;
        while l < r {
            if l & 1 == 1 {
                vl = M::op(&vl, &self.buf[l]);
                l += 1;
            }
            if r & 1 == 1 {
                r -= 1;
                vr = M::op(&self.buf[r], &vr);
            }
            l >>= 1;
            r >>= 1;
        }
        M::op(&vl, &vr)
    }
}
struct MIN;
impl Monoid for MIN {
    type T = u32;
    fn id() -> Self::T {
        (1 << 31) - 1
    }
    fn op(a: &Self::T, b: &Self::T) -> Self::T {
        std::cmp::min(*a, *b)
    }
}
fn solve() {
    input! {
        N: usize, L: usize,
        A: [u32; N],
    }

    let out = stdout();
    let mut out = BufWriter::new(out.lock());

    let mut seg: SEG<MIN> = SEG::new(N);
    for i in 0..N {
        seg.update(i, A[i]);
    }

    let mut ret = vec![];
    for i in 0..N-L+1 {
        let x = seg.query(i, i+L);
        ret.push(x);
    }
    writeln!(out, "{}", ret.iter().map(|x| x.to_string()).collect::<Vec<String>>().connect(" ")).unwrap();
}