#1148380 (Rust) No.3026 Range LCM (Online Version)

• 問題: No.3026 Range LCM (Online Version)
• ユーザー: 👑 ArcAki
• 提出日時: 2026-02-16 22:29:18
• 言語: Rust (1.93.0 + proconio + num + itertools)
• 結果: AC
• 実行時間: 835 ms / 3,000 ms
• コード長: 14,339 bytes
• コンパイル時間: 2,418 ms
• コンパイル使用メモリ: 222,788 KB
• 実行使用メモリ: 288,104 KB
• 最終ジャッジ日時: 2026-02-16 22:29:57
• 合計ジャッジ時間: 32,131 ms
• ジャッジサーバーID （参考情報）: judge4 / judge2

ファイルパターン	結果
sample	AC * 1
other	AC * 37

ソースコード

#[allow(unused_imports)]
use std::{
    convert::{Infallible, TryFrom, TryInto as _}, fmt::{self, Debug, Display, Formatter,},
    fs::File, hash::{Hash, Hasher, BuildHasherDefault}, iter::{Product, Sum}, marker::PhantomData,
    ops::{Add, AddAssign, Sub, SubAssign, Div, DivAssign, Mul, MulAssign, Neg, RangeBounds},
    str::FromStr, sync::{atomic::{self, AtomicU32, AtomicU64}, Once},
    collections::{*, btree_set::Range, btree_map::Range as BTreeRange}, mem::{swap},
    cmp::{self, Reverse, Ordering, Eq, PartialEq, PartialOrd},
    thread::LocalKey, f64::consts::PI, time::Instant, cell::RefCell,
    io::{self, stdin, Read, read_to_string, BufWriter, BufReader, stdout, Write},
};
pub mod fxhash {
    use std::hash::BuildHasherDefault;
    const K: u64 = 0x517c_c1b7_2722_0a95;
    #[derive(Default)]
    pub struct FxHasher {
        pub hash: u64,
    }
    impl FxHasher {
        #[inline(always)]
        fn mix_u64(mut h: u64, x: u64) -> u64 {
            h = h.rotate_left(5) ^ x;
            h = h.wrapping_mul(K);
            let x2 = x ^ (x >> 33) ^ (x << 11);
            h = h.rotate_left(5) ^ x2;
            h = h.wrapping_mul(K);
            h
        }

        #[inline(always)]
        fn write_u64_impl(&mut self, x: u64) {
            self.hash = Self::mix_u64(self.hash, x);
        }
    }

    impl std::hash::Hasher for FxHasher {
        #[inline(always)]
        fn finish(&self) -> u64 {
            self.hash
        }

        #[inline(always)]
        fn write(&mut self, bytes: &[u8]) {
            let mut h = self.hash;
            for &b in bytes {
                h = h.rotate_left(5) ^ (b as u64);
                h = h.wrapping_mul(K);
            }
            self.hash = h;
        }

        #[inline(always)]
        fn write_u64(&mut self, i: u64) { self.write_u64_impl(i); }
        #[inline(always)]
        fn write_u32(&mut self, i: u32) { self.write_u64_impl(i as u64); }
        #[inline(always)]
        fn write_u16(&mut self, i: u16) { self.write_u64_impl(i as u64); }
        #[inline(always)]
        fn write_u8 (&mut self, i: u8 ) { self.write_u64_impl(i as u64); }
        #[inline(always)]
        fn write_usize(&mut self, i: usize) { self.write_u64_impl(i as u64); }
        #[inline(always)]
        fn write_i64(&mut self, i: i64) { self.write_u64_impl(i as u64); }
        #[inline(always)]
        fn write_i32(&mut self, i: i32) { self.write_u64_impl(i as u64); }
        #[inline(always)]
        fn write_i16(&mut self, i: i16) { self.write_u64_impl(i as u64); }
        #[inline(always)]
        fn write_i8 (&mut self, i: i8 ) { self.write_u64_impl(i as u64); }
        #[inline(always)]
        fn write_isize(&mut self, i: isize) { self.write_u64_impl(i as u64); }
    }

    pub type FxBuildHasher = BuildHasherDefault<FxHasher>;
    pub type FxMap<K, V> = std::collections::HashMap<K, V, FxBuildHasher>;
    pub type FxSet<K> = std::collections::HashSet<K, FxBuildHasher>;
}

pub fn gcd(mut a: i64, mut b: i64)->i64{if a==0{return b;}else if b==0{return a;}let l1 = a.trailing_zeros();let l2 = b.trailing_zeros();
a >>= l1; b >>= l2;while a!=b{let x = (a^b).trailing_zeros();if a<b{swap(&mut a, &mut b)}a = (a-b)>>x;}a << l1.min(l2)}
pub fn factorial_i64(n: usize)->(Vec<i64>, Vec<i64>){ 
    let mut res = vec![1; n+1];let mut inv = vec![1; n+1];for i in 0..n{ res[i+1] = (res[i]*(i+1)as i64)%MOD; }
    inv[n] = mod_inverse(res[n], MOD);for i in (0..n).rev(){ inv[i] = inv[i+1]*(i+1) as i64%MOD; }(res, inv) }
pub fn floor(a:i64, b:i64)->i64{let res=(a%b+b)%b;(a-res)/b}
pub fn modulo(a: i64, b: i64)->i64{(a%b+b)%b}
pub fn extended_gcd(a:i64,b:i64)->(i64,i64,i64)
{if b==0{(a,1,0)}else{let(g,x,y)=extended_gcd(b,a%b);(g,y,x-floor(a,b)*y)}}
pub fn mod_inverse(a:i64,m:i64)->i64{let(_,x,_) =extended_gcd(a,m);(x%m+m)%m}
pub fn comb(a: i64, b: i64, f: &Vec<(i64, i64)>)->i64{
    if a<b{return 0;}else if b==0 || a==b{ return 1; }
    else{let x=f[a as usize].0;
        let y=f[(a-b) as usize].1;let z=f[b as usize].1;return((x*y)%MOD)*z%MOD;}}
pub fn factorial(x: i64)->Vec<(i64, i64)>{
    let mut f=vec![(1i64,1i64),(1, 1)];let mut z = 1i64;
    let mut inv = vec![0; x as usize+10];inv[1] = 1;
    for i in 2..x+1{z=(z*i)%MOD;
        let w=(MOD-inv[(MOD%i)as usize]*(MOD/i)%MOD)%MOD;
        inv[i as usize] = w;
        f.push((z, (f[i as usize-1].1*w)%MOD));}return f;}
pub fn fast_mod_pow(mut x: i64,p: usize, m: i64)->i64{
    x %= m;
    let mut res=1;let mut t=x;let mut z=p;while z > 0{
        if z%2==1{res = (res*t)%m;}t = (t*t)%m;z /= 2; }res}

pub trait SortD{ fn sort_d(&mut self); }
impl<T: Ord> SortD for Vec<T>{ fn sort_d(&mut self) {self.sort_by(|u, v| v.cmp(&u));} }
pub trait Mx{fn max(&self, rhs: Self)->Self;}
impl Mx for f64{ fn max(&self, rhs: Self)->Self{if *self < rhs{ rhs } else { *self } }}
pub trait Mi{ fn min(&self, rhs: Self)->Self; }
impl Mi for f64{ fn min(&self, rhs: Self)->Self{ if *self > rhs{ rhs } else { *self } } }
pub trait Chmax: PartialOrd + Copy {fn chmax(&mut self, rhs: Self) {if *self < rhs { *self = rhs; }}}
impl<T: PartialOrd + Copy> Chmax for T {}
pub trait Chmin: PartialOrd + Copy {fn chmin(&mut self, rhs: Self) {if *self > rhs { *self = rhs; }}}
impl<T: PartialOrd + Copy> Chmin for T {}

#[allow(unused)]
use proconio::{*, marker::*};

#[allow(dead_code)]
const INF: i64 = 1<<60;
#[allow(dead_code)]
const I: i32 = 1<<30;
#[allow(dead_code)]
const MOD: i64 = 998244353;
#[allow(dead_code)]
const D: [(usize, usize); 4] = [(1, 0), (0, 1), (!0, 0), (0, !0)];
#[allow(dead_code)]
pub fn c2d(c: u8)->(usize, usize){match c{b'U'=>(!0,0),b'D'=>(1,0),b'L'=>(0,!0),b'R'=>(0,1),_=>unreachable!()}}
#[allow(dead_code)]
pub fn c2d_i64(c: u8)->(i64, i64){match c{b'U'=>(-1,0),b'D'=>(1,0),b'L'=>(0,-1),b'R'=>(0,1),_=>unreachable!()}}
#[allow(dead_code)]
const D2: [(usize, usize); 8] = [(1, 0), (1, 1), (0, 1), (!0, 1), (!0, 0), (!0, !0), (0, !0), (1, !0)];

pub trait SegtreeMonoid {
    type S: Clone;
    fn identity() -> Self::S;
    fn op(a: &Self::S, b: &Self::S) -> Self::S;
}

#[derive(Clone, Debug)]
pub struct SegtreeNode<S: Clone>{
    val: S,
    left: u32,
    right: u32,
}

#[derive(Debug)]
pub struct PersistentSegtree<M: SegtreeMonoid>{
    n: usize,
    data: Vec<SegtreeNode<M::S>>,
    root: Vec<u32>,
}

impl<M: SegtreeMonoid> PersistentSegtree<M> {
    pub fn new(mut n: usize) -> Self {
        n = n.next_power_of_two();
        let data = Vec::with_capacity(2*n);
        let mut sg = Self {
            n, data, root: Vec::new(),
        };
        let r = sg.init(0, n);
        sg.root.push(r as u32);
        sg
    }

        pub fn new_with_q(mut n: usize, q: usize) -> Self {
        n = n.next_power_of_two();
        let data = Vec::with_capacity(2*n+q*20);
        let mut sg = Self {
            n, data, root: Vec::new(),
        };
        let r = sg.init(0, n);
        sg.root.push(r as u32);
        sg
    }

    pub fn build(a: &[M::S]) -> Self {
        let n = a.len().next_power_of_two();
        let data = Vec::with_capacity(2*n);
        let mut sg = Self {
            n, data, root: Vec::new(),
        };
        let r = sg.init_s(a, 0, n);
        sg.root.push(r as u32);
        sg
    }

    #[inline(always)]
    fn push_node(&mut self, node: SegtreeNode<M::S>)->usize{
        let r = self.data.len();
        self.data.push(node);
        r
    }

    #[inline(always)]
    fn init(&mut self, l: usize, r: usize)->usize{
        if l+1==r{
            return self.push_node(SegtreeNode { val: M::identity(), left: !0, right: !0 });
        }
        let m = (l+r)>>1;
        let left = self.init(l, m);
        let right = self.init(m, r);
        let val = M::op(&self.data[left].val, &self.data[right].val);
        self.push_node(SegtreeNode { val, left: left as u32, right: right as u32 })
    }

    #[inline(always)]
    fn init_s(&mut self, a: &[M::S], l: usize, r: usize)->usize{
        if l+1==r{
            return self.push_node(SegtreeNode { val: if l < a.len(){a[l].clone()}else{M::identity()}, left: !0, right: !0 });
        }
        let m = (l+r)>>1;
        let left = self.init_s(a, l, m);
        let right = self.init_s(a, m, r);
        let val = M::op(&self.data[left].val, &self.data[right].val);
        self.push_node(SegtreeNode { val, left: left as u32, right: right as u32 })
    }

    #[inline]
    pub fn versions(&self) -> usize {
        self.root.len()
    }

    #[inline]
    pub fn update(&mut self, t: usize, p: usize, x: M::S){
        let nr = self.update_dfs(self.root[t] as usize, 0, self.n, p, &x);
        self.root.push(nr as u32);
    }

    #[inline(always)]
    fn update_dfs(&mut self, cur: usize, l: usize, r: usize, p: usize, x: &M::S)->usize{
        if l+1==r{
            return self.push_node(SegtreeNode { val: x.clone(), left: !0, right: !0 });
        }
        let m = (l+r)>>1;
        let pre = &self.data[cur];
        let (cl, cr) = (pre.left, pre.right);
        let (nl, nr) = if p < m{
            let nl = self.update_dfs(cl as usize, l, m, p, x) as u32;
            (nl, cr)
        } else {
            let nr = self.update_dfs(cr as usize, m, r, p, x)as u32;
            (cl, nr)
        };
        self.push_node(SegtreeNode { val: M::op(&self.data[nl as usize].val, &self.data[nr as usize].val), left: nl, right: nr })
    }

    #[inline]
    pub fn prod(&self, t: usize, l: usize, r: usize) -> M::S {
        self.prod_dfs(self.root[t]as usize, 0, self.n, l, r)
    }

    #[inline(always)]
    fn prod_dfs(&self, cur: usize, cl: usize, cr: usize, l: usize, r: usize) -> M::S {
        if r <= cl || cr <= l{
            return M::identity();
        } else if l <= cl && cr <= r {
            return self.data[cur].val.clone();
        }
        let m = (cl+cr)/2;
        let node = &self.data[cur];
        let ln = self.prod_dfs(node.left as usize, cl, m, l, r);
        let rn = self.prod_dfs(node.right as usize, m, cr, l, r);
        M::op(&ln, &rn)
    }

    #[inline]
    pub fn min_left<F>(&self, t: usize, r: usize, f: F) -> usize where F: Fn(&M::S)->bool{
        assert!(f(&M::identity()));
        if r==0{return 0;}
        let mut ac = M::identity();
        self.min_left_dfs(self.root[t] as usize, 0, self.n, r, &mut ac, &f)
    }

    #[inline]
    pub fn max_right<F>(&self, t: usize, l: usize, f: F) -> usize where F: Fn(&M::S)->bool{
        assert!(f(&M::identity()));
        if l==self.n{return self.n;}
        let mut ac = M::identity();
        self.max_right_dfs(self.root[t] as usize, 0, self.n, l, &mut ac, &f)
    }

    fn min_left_dfs<F>(&self, cur: usize, l: usize, r: usize, x: usize, ac: &mut M::S, f: &F) -> usize where F: Fn(&M::S)->bool{
        if x <= l {return l;}
        if r <= x{
            let m = M::op(&self.data[cur].val, ac);
            if f(&m){
                *ac = m;
                return l;
            } else if r-l==1{
                return r;
            }
        }
        let m = (l+r)>>1;
        let node = &self.data[cur];
        let ret = self.min_left_dfs(node.right as usize, m, r, x, ac, f);
        if ret > m{
            return ret;
        }
        self.min_left_dfs(node.left as usize, l, m, x, ac, f)
    }

    fn max_right_dfs<F>(&self, cur: usize, l: usize, r: usize, x: usize, ac: &mut M::S, f: &F) -> usize where F: Fn(&M::S)->bool{
        if r <= x{return x;}
        if x <= l{
            let m = M::op(ac, &self.data[cur].val);
            if f(&m){
                *ac = m;
                return r;
            }
            if l+1==r{
                return l;
            }
        }
        let m = (l+r)>>1;
        let node = &self.data[cur];
        let (ln, rn) = (node.left, node.right);
        let ret = self.max_right_dfs(ln as usize, l, m, x, ac, f);
        if ret < m{
            return ret;
        }
        self.max_right_dfs(rn as usize, m, r, x, ac, f)
    }

    pub fn get(&self, t: usize, p: usize) -> M::S {
        self.prod(t, p, p+1)
    }
}

struct M;
impl SegtreeMonoid for M{
    type S = i64;

    fn identity() -> Self::S {
        1
    }

    fn op(&a: &Self::S, &b: &Self::S) -> Self::S {
        a*b%MOD
    }
}

pub fn linear_sieve(mx: usize)->Vec<usize>{
    let mut ps = (0..=mx).collect::<Vec<_>>();
    for i in 2..=mx{
        if ps[i]==i{
            for j in (i..).take_while(|j| i*j <= mx){
                ps[i*j] = i;
            }
        }
    }
    ps
}

const MULTI: bool = false;
#[fastout]
fn solve(){
    input!{
        n: usize,
        a: [usize; n],
        q: usize,
    }
    const MX: usize = 200000;
    let lpf = linear_sieve(MX);
    let mut s = vec![Vec::<(usize, usize)>::new(); MX];
    let mut seg = PersistentSegtree::<M>::new(n);
    let mut ts = vec![0; n];
    let mut now = vec![1; n];
    let mut ch = Vec::with_capacity(n);
    let mut ti = 0;
    for (i, &v) in a.iter().enumerate().rev(){
        let mut x = v;
        while x > 1{
            let d = lpf[x];
            let mut e = 0;
            while x%d==0{
                x /= d;
                e += 1;
            }
            let mut ac = 0;
            while let Some((i, r))=s[d].pop(){
                if ac+r >= e{
                    ch.push(i);
                    now[i] = (now[i]*fast_mod_pow(mod_inverse(d as i64, MOD), e-ac, MOD))%MOD;
                    if ac+r > e{
                        s[d].push((i, ac+r-e));
                    }
                    break;
                } else {
                    ch.push(i);
                    now[i] = (now[i]*fast_mod_pow(mod_inverse(d as i64, MOD), r, MOD))%MOD;
                    ac += r;
                }
            }
            s[d].push((i, e));
        }
        now[i] = v as i64;
        ch.push(i);ch.sort_unstable();ch.dedup();
        for &idx in &ch{
            seg.update(ti, idx, now[idx]);
            ti += 1;
        }
        ts[i] = ti;
        ch.clear();
    }
    let mut ans = 1;
    for _ in 0..q{
        input!{
            g: i64, h: i64,
        }
        let y = ((g*ans)%MOD)as usize%n+1;
        let w = ((h*ans)%MOD)as usize%n+1;
        let (l, r) = (y.min(w)-1, y.max(w));
        let t = ts[l];
        ans = seg.prod(t, l, r);
        println!("{}", ans);
    }
}

fn main() {
    if MULTI{
        input!{
            t: usize,
        }
        for _ in 0..t{
            solve();
        }
    } else {
        solve();
    }
}