// 
pub mod solution {
//{"name":"i","group":"Manual","url":"","interactive":false,"timeLimit":2000,"tests":[{"input":"","output":""}],"testType":"single","input":{"type":"stdin","fileName":null,"pattern":null},"output":{"type":"stdout","fileName":null,"pattern":null},"languages":{"java":{"taskClass":"i"}}}

use std::time::Instant;

#[allow(unused)]
use crate::dbg;
use crate::algo_lib::io::input::Input;
use crate::algo_lib::io::output::Output;
use crate::algo_lib::misc::binary_search::binary_search_first_true;
use crate::algo_lib::misc::rand::Random;
use crate::algo_lib::seg_trees::bottom_up_seg_tree::BottomUpSegTree;
use crate::algo_lib::seg_trees::lazy_seg_tree_max::MaxValNode;
use crate::algo_lib::seg_trees::lazy_seg_tree_max::SegTreeMax;

#[derive(Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Default)]
struct Query {
    r: usize,
    l: usize,
    id: usize,
}

// type ST = SegTreeMax<Query>;
type ST = BottomUpSegTree<MaxValNode<Query>>;

fn stress() {
    for tc in 1.. {
        dbg!(tc);
        let start = Instant::now();
        let mut rnd = Random::new(tc);
        let n = rnd.gen(1..10);
        const MAX: usize = 1_000_000;
        let mut a = rnd.gen_vec(n, 1..MAX);
        let mut queries = vec![];
        let queries_n = rnd.gen(1..10);
        for id in 0..queries_n {
            let l = rnd.gen(0..n);
            let r = rnd.gen(l..n);
            queries.push(Query { l, r, id: id + 1 });
        }
        let res1 = solve_case(&a, &queries);
        dbg!(start.elapsed());
    }
}

fn solve(input: &mut Input, out: &mut Output, _test_case: usize) {
    let n = input.usize();
    let q = input.usize();
    let a = input.vec::<usize>(n);

    let mut queries = Vec::with_capacity(q);
    for i in 0..q {
        let l = input.usize();
        let r = input.usize();
        queries.push(Query {
            l: l - 1,
            r: r - 1,
            id: i + 1,
        });
    }

    let results = solve_case(&a, &queries);

    for x in results {
        out.println(x);
    }
}

fn solve_case(a: &[usize], queries: &[Query]) -> Vec<usize> {
    let n = a.len();
    let max_a = *a.iter().max().unwrap();
    let mut positions = vec![vec![]; max_a + 1];
    for i in 0..n {
        positions[a[i]].push(i);
    }
    let mut queries_by_l = vec![vec![]; n];
    for q in queries.iter() {
        queries_by_l[q.l].push(*q);
    }
    for i in 0..n {
        queries_by_l[i].sort_by_key(|q| q.r);
    }
    let empty_query = Query { l: 0, r: 0, id: 0 };
    let mut seg_tree = ST::new(n, |pos| {
        let query = if queries_by_l[pos].is_empty() {
            empty_query
        } else {
            *queries_by_l[pos].last().unwrap()
        };
        MaxValNode {
            max_val: query,
            pos,
        }
    });
    let mut results = vec![0; queries.len()];
    for gcd in (1..=max_a).rev() {
        let mut cur_pos = vec![];
        for mult in 1.. {
            let value = mult * gcd;
            if value > max_a {
                break;
            }
            cur_pos.extend_from_slice(&positions[value]);
        }
        cur_pos.sort_unstable();
        for i in 1..cur_pos.len() {
            let mid = cur_pos[i];
            let prev = cur_pos[i - 1];
            let right_bound = mid + (mid - prev);
            let right_pos =
                binary_search_first_true(i + 1..cur_pos.len(), |i| cur_pos[i] >= right_bound);
            if right_pos == cur_pos.len() {
                continue;
            }
            let right_bound = cur_pos[right_pos];
            loop {
                let query = seg_tree.get(0..prev + 1).max_val;
                if query != empty_query && query.r >= right_bound {
                    results[query.id - 1] = gcd;
                    queries_by_l[query.l].pop();
                    {
                        let next_query = if queries_by_l[query.l].is_empty() {
                            empty_query
                        } else {
                            *queries_by_l[query.l].last().unwrap()
                        };
                        seg_tree.update_point(
                            query.l,
                            MaxValNode {
                                max_val: next_query,
                                pos: query.l,
                            },
                        );
                    }
                } else {
                    break;
                }
            }
        }
    }
    results
}

pub(crate) fn run(mut input: Input, mut output: Output) -> bool {
    solve(&mut input, &mut output, 1);
    output.flush();
    true
}

}
pub mod algo_lib {
pub mod io {
pub mod input {
use std::fmt::Debug;
use std::io::Read;
use std::marker::PhantomData;
use std::path::Path;
use std::str::FromStr;

pub struct Input {
    input: Box<dyn Read>,
    buf: Vec<u8>,
    at: usize,
    buf_read: usize,
}

macro_rules! read_integer_fun {
    ($t:ident) => {
        #[allow(unused)]
        pub fn $t(&mut self) -> $t {
            self.read_integer()
        }
    };
}

impl Input {
    const DEFAULT_BUF_SIZE: usize = 4096;

    ///
    /// Using with stdin:
    /// ```no_run
    /// use algo_lib::io::input::Input;
    /// let stdin = std::io::stdin();
    /// let input = Input::new(Box::new(stdin));
    /// ```
    ///
    /// For read files use ``new_file`` instead.
    ///
    ///
    pub fn new(input: Box<dyn Read>) -> Self {
        Self {
            input,
            buf: vec![0; Self::DEFAULT_BUF_SIZE],
            at: 0,
            buf_read: 0,
        }
    }

    pub fn new_stdin() -> Self {
        let stdin = std::io::stdin();
        Self::new(Box::new(stdin))
    }

    pub fn new_file<P: AsRef<Path>>(path: P) -> Self {
        let file = std::fs::File::open(&path)
            .unwrap_or_else(|_| panic!("Can't open file: {:?}", path.as_ref().as_os_str()));
        Self::new(Box::new(file))
    }

    pub fn new_with_size(input: Box<dyn Read>, buf_size: usize) -> Self {
        Self {
            input,
            buf: vec![0; buf_size],
            at: 0,
            buf_read: 0,
        }
    }

    pub fn new_file_with_size<P: AsRef<Path>>(path: P, buf_size: usize) -> Self {
        let file = std::fs::File::open(&path)
            .unwrap_or_else(|_| panic!("Can't open file: {:?}", path.as_ref().as_os_str()));
        Self::new_with_size(Box::new(file), buf_size)
    }

    pub fn get(&mut self) -> Option<u8> {
        if self.refill_buffer() {
            let res = self.buf[self.at];
            self.at += 1;
            Some(res)
        } else {
            None
        }
    }

    pub fn peek(&mut self) -> Option<u8> {
        if self.refill_buffer() {
            Some(self.buf[self.at])
        } else {
            None
        }
    }

    pub fn skip_whitespace(&mut self) {
        while let Some(b) = self.peek() {
            if !char::from(b).is_whitespace() {
                return;
            }
            self.get();
        }
    }

    pub fn next_token(&mut self) -> Option<Vec<u8>> {
        self.skip_whitespace();
        let mut res = Vec::new();
        while let Some(c) = self.get() {
            if char::from(c).is_whitespace() {
                break;
            }
            res.push(c);
        }
        if res.is_empty() {
            None
        } else {
            Some(res)
        }
    }

    //noinspection RsSelfConvention
    pub fn is_exhausted(&mut self) -> bool {
        self.peek().is_none()
    }

    pub fn has_more_elements(&mut self) -> bool {
        !self.is_exhausted()
    }

    pub fn read<T: Readable>(&mut self) -> T {
        T::read(self)
    }

    pub fn vec<T: Readable>(&mut self, size: usize) -> Vec<T> {
        let mut res = Vec::with_capacity(size);
        for _ in 0usize..size {
            res.push(self.read());
        }
        res
    }

    pub fn string_vec(&mut self, size: usize) -> Vec<Vec<u8>> {
        let mut res = Vec::with_capacity(size);
        for _ in 0usize..size {
            res.push(self.string());
        }
        res
    }

    pub fn read_line(&mut self) -> String {
        let mut res = String::new();
        while let Some(c) = self.get() {
            if c == b'\n' {
                break;
            }
            if c == b'\r' {
                if self.peek() == Some(b'\n') {
                    self.get();
                }
                break;
            }
            res.push(c.into());
        }
        res
    }

    #[allow(clippy::should_implement_trait)]
    pub fn into_iter<T: Readable>(self) -> InputIterator<T> {
        InputIterator {
            input: self,
            phantom: Default::default(),
        }
    }

    fn read_integer<T: FromStr + Debug>(&mut self) -> T
    where
        <T as FromStr>::Err: Debug,
    {
        let res = self.read_string();
        res.parse::<T>().unwrap()
    }

    fn read_string(&mut self) -> String {
        match self.next_token() {
            None => {
                panic!("Input exhausted");
            }
            Some(res) => unsafe { String::from_utf8_unchecked(res) },
        }
    }

    pub fn string_as_string(&mut self) -> String {
        self.read_string()
    }

    pub fn string(&mut self) -> Vec<u8> {
        self.read_string().into_bytes()
    }

    fn read_char(&mut self) -> char {
        self.skip_whitespace();
        self.get().unwrap().into()
    }

    fn read_float(&mut self) -> f64 {
        self.read_string().parse().unwrap()
    }

    pub fn f64(&mut self) -> f64 {
        self.read_float()
    }

    fn refill_buffer(&mut self) -> bool {
        if self.at == self.buf_read {
            self.at = 0;
            self.buf_read = self.input.read(&mut self.buf).unwrap();
            self.buf_read != 0
        } else {
            true
        }
    }

    read_integer_fun!(i32);
    read_integer_fun!(i64);
    read_integer_fun!(i128);
    read_integer_fun!(u32);
    read_integer_fun!(u64);
    read_integer_fun!(usize);
}

pub trait Readable {
    fn read(input: &mut Input) -> Self;
}

impl Readable for String {
    fn read(input: &mut Input) -> Self {
        input.read_string()
    }
}

impl Readable for char {
    fn read(input: &mut Input) -> Self {
        input.read_char()
    }
}

impl Readable for f64 {
    fn read(input: &mut Input) -> Self {
        input.read_string().parse().unwrap()
    }
}

impl Readable for f32 {
    fn read(input: &mut Input) -> Self {
        input.read_string().parse().unwrap()
    }
}

impl<T: Readable> Readable for Vec<T> {
    fn read(input: &mut Input) -> Self {
        let size = input.read();
        input.vec(size)
    }
}

pub struct InputIterator<T: Readable> {
    input: Input,
    phantom: PhantomData<T>,
}

impl<T: Readable> Iterator for InputIterator<T> {
    type Item = T;

    fn next(&mut self) -> Option<Self::Item> {
        self.input.skip_whitespace();
        self.input.peek().map(|_| self.input.read())
    }
}

macro_rules! read_integer {
    ($t:ident) => {
        impl Readable for $t {
            fn read(input: &mut Input) -> Self {
                input.read_integer()
            }
        }
    };
}

read_integer!(i8);
read_integer!(i16);
read_integer!(i32);
read_integer!(i64);
read_integer!(i128);
read_integer!(isize);
read_integer!(u8);
read_integer!(u16);
read_integer!(u32);
read_integer!(u64);
read_integer!(u128);
read_integer!(usize);
}
pub mod output {
use std::io::Write;

pub struct Output {
    output: Box<dyn Write>,
    buf: Vec<u8>,
    at: usize,
    auto_flush: bool,
}

impl Output {
    const DEFAULT_BUF_SIZE: usize = 4096;

    pub fn new(output: Box<dyn Write>) -> Self {
        Self {
            output,
            buf: vec![0; Self::DEFAULT_BUF_SIZE],
            at: 0,
            auto_flush: false,
        }
    }

    pub fn new_stdout() -> Self {
        let stdout = std::io::stdout();
        Self::new(Box::new(stdout))
    }

    pub fn new_file(path: impl AsRef<std::path::Path>) -> Self {
        let file = std::fs::File::create(path).unwrap();
        Self::new(Box::new(file))
    }

    pub fn new_with_auto_flush(output: Box<dyn Write>) -> Self {
        Self {
            output,
            buf: vec![0; Self::DEFAULT_BUF_SIZE],
            at: 0,
            auto_flush: true,
        }
    }

    pub fn flush(&mut self) {
        if self.at != 0 {
            self.output.write_all(&self.buf[..self.at]).unwrap();
            self.at = 0;
            self.output.flush().expect("Couldn't flush output");
        }
    }

    pub fn print<T: Writable>(&mut self, s: T) {
        s.write(self);
    }

    pub fn println<T: Writable>(&mut self, s: T) {
        s.write(self);
        self.put(b'\n');
    }

    pub fn put(&mut self, b: u8) {
        self.buf[self.at] = b;
        self.at += 1;
        if self.at == self.buf.len() {
            self.flush();
        }
    }

    pub fn maybe_flush(&mut self) {
        if self.auto_flush {
            self.flush();
        }
    }

    pub fn print_per_line<T: Writable>(&mut self, arg: &[T]) {
        for i in arg {
            i.write(self);
            self.put(b'\n');
        }
    }

    pub fn print_iter<T: Writable, I: Iterator<Item = T>>(&mut self, iter: I) {
        let mut first = true;
        for e in iter {
            if first {
                first = false;
            } else {
                self.put(b' ');
            }
            e.write(self);
        }
    }

    pub fn print_iter_ref<'a, T: 'a + Writable, I: Iterator<Item = &'a T>>(&mut self, iter: I) {
        let mut first = true;
        for e in iter {
            if first {
                first = false;
            } else {
                self.put(b' ');
            }
            e.write(self);
        }
    }
}

impl Write for Output {
    fn write(&mut self, buf: &[u8]) -> std::io::Result<usize> {
        let mut start = 0usize;
        let mut rem = buf.len();
        while rem > 0 {
            let len = (self.buf.len() - self.at).min(rem);
            self.buf[self.at..self.at + len].copy_from_slice(&buf[start..start + len]);
            self.at += len;
            if self.at == self.buf.len() {
                self.flush();
            }
            start += len;
            rem -= len;
        }
        if self.auto_flush {
            self.flush();
        }
        Ok(buf.len())
    }

    fn flush(&mut self) -> std::io::Result<()> {
        self.flush();
        Ok(())
    }
}

pub trait Writable {
    fn write(&self, output: &mut Output);
}

impl Writable for &str {
    fn write(&self, output: &mut Output) {
        output.write_all(self.as_bytes()).unwrap();
    }
}

impl Writable for String {
    fn write(&self, output: &mut Output) {
        output.write_all(self.as_bytes()).unwrap();
    }
}

impl Writable for char {
    fn write(&self, output: &mut Output) {
        output.put(*self as u8);
    }
}

impl<T: Writable> Writable for [T] {
    fn write(&self, output: &mut Output) {
        output.print_iter_ref(self.iter());
    }
}

impl<T: Writable> Writable for Vec<T> {
    fn write(&self, output: &mut Output) {
        self[..].write(output);
    }
}

macro_rules! write_to_string {
    ($t:ident) => {
        impl Writable for $t {
            fn write(&self, output: &mut Output) {
                self.to_string().write(output);
            }
        }
    };
}

write_to_string!(u8);
write_to_string!(u16);
write_to_string!(u32);
write_to_string!(u64);
write_to_string!(u128);
write_to_string!(usize);
write_to_string!(i8);
write_to_string!(i16);
write_to_string!(i32);
write_to_string!(i64);
write_to_string!(i128);
write_to_string!(isize);
write_to_string!(f32);
write_to_string!(f64);

impl<T: Writable, U: Writable> Writable for (T, U) {
    fn write(&self, output: &mut Output) {
        self.0.write(output);
        output.put(b' ');
        self.1.write(output);
    }
}

impl<T: Writable, U: Writable, V: Writable> Writable for (T, U, V) {
    fn write(&self, output: &mut Output) {
        self.0.write(output);
        output.put(b' ');
        self.1.write(output);
        output.put(b' ');
        self.2.write(output);
    }
}
}
}
pub mod misc {
pub mod binary_search {
use crate::algo_lib::misc::num_traits::Number;
use std::ops::Range;

pub fn binary_search_first_true<T>(range: Range<T>, mut f: impl FnMut(T) -> bool) -> T
where
    T: Number,
{
    // we can't store [range.start - 1] into [left], because it could overflow
    let mut left_plus_one = range.start;
    let mut right = range.end;
    while right > left_plus_one {
        let mid = left_plus_one + (right - left_plus_one) / T::TWO;
        if f(mid) {
            right = mid;
        } else {
            left_plus_one = mid + T::ONE;
        }
    }
    right
}

pub fn binary_search_last_true<T>(range: Range<T>, mut f: impl FnMut(T) -> bool) -> Option<T>
where
    T: Number,
{
    let first_false = binary_search_first_true(range.clone(), |x| !f(x));
    if first_false == range.start {
        None
    } else {
        Some(first_false - T::ONE)
    }
}

#[test]
fn simple_stress() {
    const N: usize = 50;
    for n in 1..N {
        for cnt_false in 0..=n {
            let mut a = vec![false; cnt_false];
            a.resize(n, true);
            let mut max_f_calls = ((n + 1) as f64).log2().ceil() as i32;
            let f_is_true = |id: usize| -> bool {
                max_f_calls -= 1;
                assert!(max_f_calls >= 0);
                a[id]
            };
            let result = binary_search_first_true(0..n, f_is_true);
            assert_eq!(result, cnt_false);
        }
    }
}
}
pub mod dbg_macro {
#[macro_export]
#[allow(unused_macros)]
macro_rules! dbg {
    ($first_val:expr, $($val:expr),+ $(,)?) => {
        eprint!("[{}:{}] {} = {:?}",
                    file!(), line!(), stringify!($first_val), &$first_val);
        ($(eprint!(", {} = {:?}", stringify!($val), &$val)),+,);
        eprintln!();
    };
    ($first_val:expr) => {
        eprintln!("[{}:{}] {} = {:?}",
                    file!(), line!(), stringify!($first_val), &$first_val)
    };
}
}
pub mod gen_vector {
pub fn gen_vec<T>(n: usize, f: impl FnMut(usize) -> T) -> Vec<T> {
    (0..n).map(f).collect()
}
}
pub mod num_traits {
use std::cmp::Ordering;
use std::fmt::Debug;
use std::ops::Add;
use std::ops::AddAssign;
use std::ops::Div;
use std::ops::DivAssign;
use std::ops::Mul;
use std::ops::MulAssign;
use std::ops::Sub;
use std::ops::SubAssign;

pub trait HasConstants<T> {
    const MAX: T;
    const MIN: T;
    const ZERO: T;
    const ONE: T;
    const TWO: T;
}

pub trait ConvSimple<T> {
    fn from_i32(val: i32) -> T;
    fn to_i32(self) -> i32;
    fn to_f64(self) -> f64;
}

pub trait Signum {
    fn signum(&self) -> i32;
}

pub trait Number:
    Copy
    + Add<Output = Self>
    + AddAssign
    + Sub<Output = Self>
    + SubAssign
    + Mul<Output = Self>
    + MulAssign
    + Div<Output = Self>
    + DivAssign
    + PartialOrd
    + PartialEq
    + HasConstants<Self>
    + Default
    + Debug
    + Sized
    + ConvSimple<Self>
{
}

impl<
        T: Copy
            + Add<Output = Self>
            + AddAssign
            + Sub<Output = Self>
            + SubAssign
            + Mul<Output = Self>
            + MulAssign
            + Div<Output = Self>
            + DivAssign
            + PartialOrd
            + PartialEq
            + HasConstants<Self>
            + Default
            + Debug
            + Sized
            + ConvSimple<Self>,
    > Number for T
{
}

macro_rules! has_constants_impl {
    ($t: ident) => {
        impl HasConstants<$t> for $t {
            // TODO: remove `std` for new rust version..
            const MAX: $t = std::$t::MAX;
            const MIN: $t = std::$t::MIN;
            const ZERO: $t = 0;
            const ONE: $t = 1;
            const TWO: $t = 2;
        }

        impl ConvSimple<$t> for $t {
            fn from_i32(val: i32) -> $t {
                val as $t
            }

            fn to_i32(self) -> i32 {
                self as i32
            }

            fn to_f64(self) -> f64 {
                self as f64
            }
        }
    };
}

has_constants_impl!(i32);
has_constants_impl!(i64);
has_constants_impl!(i128);
has_constants_impl!(u32);
has_constants_impl!(u64);
has_constants_impl!(u128);
has_constants_impl!(usize);
has_constants_impl!(u8);

impl ConvSimple<Self> for f64 {
    fn from_i32(val: i32) -> Self {
        val as f64
    }

    fn to_i32(self) -> i32 {
        self as i32
    }

    fn to_f64(self) -> f64 {
        self
    }
}

impl HasConstants<Self> for f64 {
    const MAX: Self = Self::MAX;
    const MIN: Self = -Self::MAX;
    const ZERO: Self = 0.0;
    const ONE: Self = 1.0;
    const TWO: Self = 2.0;
}

impl<T: Number + Ord> Signum for T {
    fn signum(&self) -> i32 {
        match self.cmp(&T::ZERO) {
            Ordering::Greater => 1,
            Ordering::Less => -1,
            Ordering::Equal => 0,
        }
    }
}
}
pub mod rand {
use crate::algo_lib::misc::gen_vector::gen_vec;
use crate::algo_lib::misc::num_traits::Number;
use std::ops::Range;
use std::time::SystemTime;
use std::time::UNIX_EPOCH;

#[allow(dead_code)]
pub struct Random {
    state: u64,
}

impl Random {
    pub fn gen_u64(&mut self) -> u64 {
        let mut x = self.state;
        x ^= x << 13;
        x ^= x >> 7;
        x ^= x << 17;
        self.state = x;
        x
    }

    #[allow(dead_code)]
    pub fn next_in_range(&mut self, from: usize, to: usize) -> usize {
        assert!(from < to);
        (from as u64 + self.gen_u64() % ((to - from) as u64)) as usize
    }

    pub fn gen_index<T>(&mut self, a: &[T]) -> usize {
        self.gen(0..a.len())
    }

    #[allow(dead_code)]
    #[inline(always)]
    pub fn gen_double(&mut self) -> f64 {
        (self.gen_u64() as f64) / (std::usize::MAX as f64)
    }

    #[allow(dead_code)]
    pub fn new(seed: u64) -> Self {
        let state = if seed == 0 { 787788 } else { seed };
        Self { state }
    }

    pub fn new_time_seed() -> Self {
        let time = SystemTime::now();
        let seed = (time.duration_since(UNIX_EPOCH).unwrap().as_nanos() % 1_000_000_000) as u64;
        if seed == 0 {
            Self::new(787788)
        } else {
            Self::new(seed)
        }
    }

    #[allow(dead_code)]
    pub fn gen_permutation(&mut self, n: usize) -> Vec<usize> {
        let mut result: Vec<_> = (0..n).collect();
        for i in 0..n {
            let idx = self.next_in_range(0, i + 1);
            result.swap(i, idx);
        }
        result
    }

    pub fn shuffle<T>(&mut self, a: &mut [T]) {
        for i in 1..a.len() {
            a.swap(i, self.gen(0..i + 1));
        }
    }

    pub fn gen<T>(&mut self, range: Range<T>) -> T
    where
        T: Number,
    {
        let from = T::to_i32(range.start);
        let to = T::to_i32(range.end);
        assert!(from < to);
        let len = (to - from) as usize;
        T::from_i32(self.next_in_range(0, len) as i32 + from)
    }

    pub fn gen_vec<T>(&mut self, n: usize, range: Range<T>) -> Vec<T>
    where
        T: Number,
    {
        gen_vec(n, |_| self.gen(range.clone()))
    }

    pub fn gen_nonempty_range(&mut self, n: usize) -> Range<usize> {
        let x = self.gen(0..n);
        let y = self.gen(0..n);
        if x <= y {
            x..y + 1
        } else {
            y..x + 1
        }
    }

    pub fn gen_bool(&mut self) -> bool {
        self.gen(0..2) == 0
    }
}
}
}
pub mod seg_trees {
pub mod bottom_up_seg_tree {
use std::ops::Range;

use crate::algo_lib::seg_trees::seg_tree_trait::SegTreeNode;

pub struct BottomUpSegTree<Node: SegTreeNode> {
    n: usize,
    nodes: Vec<Node>,
    context: Node::Context,
}

impl<Node: SegTreeNode> BottomUpSegTree<Node> {
    pub fn new(start_n: usize, f: impl Fn(usize) -> Node) -> Self
    where
        Node::Context: Default,
    {
        let n = start_n.next_power_of_two();
        let mut res = Self {
            n,
            nodes: vec![Node::default(); 2 * n],
            context: Default::default(),
        };
        for i in 0..start_n {
            res.nodes[n + i] = f(i);
        }
        for i in (1..n).rev() {
            res.nodes[i] = Node::join_nodes(&res.nodes[2 * i], &res.nodes[2 * i + 1], &res.context);
        }
        res
    }

    pub fn update_point(&mut self, pos: usize, v: Node) {
        let mut i = pos + self.n;
        self.nodes[i] = v;
        while i > 1 {
            i /= 2;
            self.nodes[i] =
                Node::join_nodes(&self.nodes[2 * i], &self.nodes[2 * i + 1], &self.context);
        }
    }

    pub fn get_root(&self) -> &Node {
        &self.nodes[1]
    }

    pub fn get(&self, range: Range<usize>) -> Node {
        let mut l = range.start + self.n;
        let mut r = range.end + self.n;
        let mut res_l = Node::default();
        let mut res_r = Node::default();
        while l < r {
            if l & 1 != 0 {
                res_l = Node::join_nodes(&res_l, &self.nodes[l], &self.context);
                l += 1;
            }
            if r & 1 != 0 {
                r -= 1;
                res_r = Node::join_nodes(&self.nodes[r], &res_r, &self.context);
            }
            l /= 2;
            r /= 2;
        }
        Node::join_nodes(&res_l, &res_r, &self.context)
    }
}
}
pub mod lazy_seg_tree {
use std::ops::Range;

use crate::algo_lib::seg_trees::seg_tree_trait::SegTreeNode;

///
/// Segment Tree
///
#[allow(unused)]
#[derive(Clone)]
pub struct SegTree<T: SegTreeNode> {
    n: usize,
    tree: Vec<T>,
    updates_to_push: Vec<Option<T::Update>>,
    context: T::Context,
    right_nodes: Vec<usize>,
}

#[allow(unused)]
impl<T: SegTreeNode> SegTree<T> {
    fn pull(&mut self, v: usize, vr: usize) {
        self.tree[v] = T::join_nodes(&self.tree[v + 1], &self.tree[vr], &self.context);
    }

    fn build(&mut self, v: usize, l: usize, r: usize, init_val: &T) {
        if l + 1 == r {
            self.tree[v] = init_val.clone();
        } else {
            let m = (l + r) >> 1;
            let vr = v + ((m - l) << 1);
            self.build(v + 1, l, m, init_val);
            self.build(vr, m, r, init_val);
            self.pull(v, vr);
        }
    }

    fn push(&mut self, v: usize, l: usize, r: usize) {
        let update = self.updates_to_push[v].clone();
        self.updates_to_push[v] = None;
        match update {
            None => {}
            Some(update) => {
                let m = (l + r) >> 1;
                self.apply_update(v + 1, &update, m - l == 1);
                self.apply_update(v + ((r - l) & !1), &update, r - m == 1);
            }
        }
    }

    fn get_(&mut self, v: usize, l: usize, r: usize, ql: usize, qr: usize) -> T {
        assert!(qr >= l);
        assert!(ql < r);
        if ql <= l && r <= qr {
            return self.tree[v].clone();
        }
        let m = (l + r) >> 1;
        let vr = v + ((m - l) << 1);
        self.push(v, l, r);
        let res = if ql >= m {
            self.get_(vr, m, r, ql, qr)
        } else if qr <= m {
            self.get_(v + 1, l, m, ql, qr)
        } else {
            T::join_nodes(
                &self.get_(v + 1, l, m, ql, qr),
                &self.get_(vr, m, r, ql, qr),
                &self.context,
            )
        };
        self.pull(v, vr);
        res
    }

    fn visit_(
        &mut self,
        v: usize,
        l: usize,
        r: usize,
        ql: usize,
        qr: usize,
        f: &mut impl FnMut(&T),
    ) {
        assert!(qr >= l);
        assert!(ql < r);
        if ql <= l && r <= qr {
            f(&self.tree[v]);
            return;
        }
        let m = (l + r) >> 1;
        let vr = v + ((m - l) << 1);
        self.push(v, l, r);
        if ql >= m {
            self.visit_(vr, m, r, ql, qr, f);
        } else if qr <= m {
            self.visit_(v + 1, l, m, ql, qr, f)
        } else {
            self.visit_(v + 1, l, m, ql, qr, f);
            self.visit_(vr, m, r, ql, qr, f);
        };
        self.pull(v, vr);
    }

    fn join_updates(current: &mut Option<T::Update>, add: &T::Update) {
        match current {
            None => *current = Some(add.clone()),
            Some(current) => T::join_updates(current, add),
        };
    }

    fn apply_update(&mut self, v: usize, update: &T::Update, is_leaf: bool) {
        T::apply_update(&mut self.tree[v], update);
        if !is_leaf {
            Self::join_updates(&mut self.updates_to_push[v], update);
        }
    }

    fn modify_(&mut self, v: usize, l: usize, r: usize, ql: usize, qr: usize, update: &T::Update) {
        assert!(qr >= l);
        assert!(ql < r);
        if ql <= l && r <= qr {
            self.apply_update(v, update, r - l == 1);
            return;
        }
        let m = (l + r) >> 1;
        let vr = v + ((m - l) << 1);
        self.push(v, l, r);
        if ql >= m {
            self.modify_(vr, m, r, ql, qr, update);
        } else if qr <= m {
            self.modify_(v + 1, l, m, ql, qr, update);
        } else {
            self.modify_(v + 1, l, m, ql, qr, update);
            self.modify_(vr, m, r, ql, qr, update);
        };
        self.pull(v, vr);
    }

    pub fn update(&mut self, range: Range<usize>, update: T::Update) {
        if range.is_empty() {
            return;
        }
        assert!(!range.is_empty());
        self.modify_(0, 0, self.n, range.start, range.end, &update);
    }

    pub fn update_point(&mut self, pos: usize, new_node: T) {
        let mut l = 0;
        let mut r = self.n;
        let mut v: usize = 0;
        let mut to_pull = vec![];
        while r - l > 1 {
            let m = (l + r) >> 1;
            let vr = v + ((m - l) << 1);
            self.push(v, l, r);
            to_pull.push((v, vr));
            if pos < m {
                r = m;
                v = v + 1;
            } else {
                l = m;
                v = vr;
            }
        }
        self.tree[v] = new_node;
        for (v, vr) in to_pull.into_iter().rev() {
            self.pull(v, vr);
        }
    }

    fn find_last_true_(
        &mut self,
        v: usize,
        l: usize,
        r: usize,
        range: Range<usize>,
        f: &impl Fn(&T) -> bool,
    ) -> Option<usize> {
        if range.start >= r || l >= range.end {
            return None;
        }
        let m = (l + r) >> 1;
        let vr = v + ((m - l) << 1);
        if range.start <= l && r <= range.end {
            if !f(&self.tree[v]) {
                return None;
            }
            if r - l == 1 {
                return Some(l);
            }
        }
        self.push(v, l, r);
        if let Some(res) = self.find_last_true_(vr, m, r, range.clone(), f) {
            Some(res)
        } else {
            self.find_last_true_(v + 1, l, m, range, f)
        }
    }

    // returns position
    pub fn find_last_true(&mut self, range: Range<usize>, f: impl Fn(&T) -> bool) -> Option<usize> {
        self.find_last_true_(0, 0, self.n, range, &f)
    }

    pub fn get(&mut self, range: Range<usize>) -> T {
        if range.is_empty() {
            return T::default();
        }
        self.get_(0, 0, self.n, range.start, range.end)
    }

    pub fn visit(&mut self, range: Range<usize>, f: &mut impl FnMut(&T)) {
        if range.is_empty() {
            return;
        }
        self.visit_(0, 0, self.n, range.start, range.end, f);
    }

    pub fn new_with_context(n: usize, f: impl Fn(usize) -> T, context: T::Context) -> Self {
        assert!(n > 0);
        let tree = vec![T::default(); 2 * n - 1];
        let updates_to_push = vec![None; 2 * n - 1];
        let mut res = SegTree {
            n,
            tree,
            updates_to_push,
            context,
            right_nodes: vec![],
        };
        res.build_f(0, 0, n, &f);
        res
    }

    pub fn new(n: usize, f: impl Fn(usize) -> T) -> Self
    where
        T::Context: Default,
    {
        assert!(n > 0);
        let tree = vec![T::default(); 2 * n - 1];
        let updates_to_push = vec![None; 2 * n - 1];
        let mut res = SegTree {
            n,
            tree,
            updates_to_push,
            context: T::Context::default(),
            right_nodes: vec![],
        };
        res.build_f(0, 0, n, &f);
        res
    }

    fn build_f(&mut self, v: usize, l: usize, r: usize, f: &impl Fn(usize) -> T) {
        if l + 1 == r {
            self.tree[v] = f(l);
        } else {
            let m = (l + r) >> 1;
            let vr = v + ((m - l) << 1);
            self.build_f(v + 1, l, m, f);
            self.build_f(vr, m, r, f);
            self.pull(v, vr);
        }
    }

    pub fn len(&self) -> usize {
        self.n
    }

    pub fn expert_get_node(&self, node: usize) -> &T {
        &self.tree[node]
    }

    pub fn expert_get_left_node(&self, node: usize) -> usize {
        node + 1
    }

    fn build_right_nodes(&mut self, v: usize, l: usize, r: usize) {
        if l + 1 == r {
            self.right_nodes.push(0);
        } else {
            let m = (l + r) >> 1;
            let vr = v + ((m - l) << 1);
            self.right_nodes.push(vr);
            self.build_right_nodes(v + 1, l, m);
            self.build_right_nodes(vr, m, r);
        }
    }

    // TODO: shouldn't be mut
    pub fn expert_get_right_node(&mut self, node: usize) -> usize {
        if self.right_nodes.is_empty() {
            self.build_right_nodes(0, 0, self.n);
        }
        self.right_nodes[node]
    }

    // Used for Kinetic Seg Tree
    pub fn expert_rebuild_nodes(&mut self, should_rebuild: impl Fn(&T, &T::Context) -> bool) {
        self.expert_rebuild_nodes_(0, 0, self.n, &should_rebuild);
    }

    fn expert_rebuild_nodes_(
        &mut self,
        v: usize,
        l: usize,
        r: usize,
        should_rebuild: &impl Fn(&T, &T::Context) -> bool,
    ) {
        if r - l <= 1 || !should_rebuild(&self.tree[v], &self.context) {
            return;
        }
        let m = (l + r) >> 1;
        let vr = v + ((m - l) << 1);
        self.push(v, l, r);

        self.expert_rebuild_nodes_(v + 1, l, m, should_rebuild);
        self.expert_rebuild_nodes_(vr, m, r, should_rebuild);

        self.pull(v, vr);
    }

    pub fn update_context(&mut self, f: impl Fn(&mut T::Context)) {
        f(&mut self.context);
    }

    pub fn get_context(&self) -> &T::Context {
        &self.context
    }
}
}
pub mod lazy_seg_tree_max {
use crate::algo_lib::seg_trees::lazy_seg_tree::SegTree;
use crate::algo_lib::seg_trees::seg_tree_trait::SegTreeNode;

#[derive(Clone, Default, Copy, Debug)]
pub struct MaxValNode<T> {
    pub max_val: T,
    pub pos: usize,
}

impl<T> SegTreeNode for MaxValNode<T>
where
    T: Default + Clone + Ord + Copy,
{
    #[allow(unused)]
    fn join_nodes(l: &Self, r: &Self, context: &()) -> Self {
        if l.max_val > r.max_val {
            *l
        } else {
            *r
        }
    }

    fn apply_update(node: &mut Self, update: &Self::Update) {
        node.max_val = *update;
    }

    #[allow(unused)]
    fn join_updates(current: &mut Self::Update, add: &Self::Update) {
        *current = *add;
    }

    type Update = T;
    type Context = ();
}

pub type SegTreeMax<T> = SegTree<MaxValNode<T>>;
}
pub mod seg_tree_trait {
pub trait SegTreeNode: Clone + Default {
    fn join_nodes(l: &Self, r: &Self, context: &Self::Context) -> Self;

    fn apply_update(node: &mut Self, update: &Self::Update);
    fn join_updates(current: &mut Self::Update, add: &Self::Update);

    type Update: Clone;
    type Context;
}
}
}
}
fn main() {
    let input = algo_lib::io::input::Input::new_stdin();
    let mut output = algo_lib::io::output::Output::new_stdout();
    crate::solution::run(input, output);
}