#818069 (Rust) No.2127 Mod, Sum, Sum, Mod

• 問題: No.2127 Mod, Sum, Sum, Mod
• ユーザー: akakimidori
• 提出日時: 2022-11-18 22:58:09
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 64 ms / 2,000 ms
• コード長: 11,102 bytes
• コンパイル時間: 12,151 ms
• コンパイル使用メモリ: 377,260 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-09-20 03:25:49
• 合計ジャッジ時間: 13,532 ms
• ジャッジサーバーID （参考情報）: judge4 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 5,248 KB
testcase_01	AC	1 ms; 5,248 KB
testcase_02	AC	62 ms; 5,376 KB
testcase_03	AC	1 ms; 5,376 KB
testcase_04	AC	1 ms; 5,376 KB
testcase_05	AC	1 ms; 5,376 KB
testcase_06	AC	1 ms; 5,376 KB
testcase_07	AC	1 ms; 5,376 KB
testcase_08	AC	0 ms; 5,376 KB
testcase_09	AC	1 ms; 5,376 KB
testcase_10	AC	1 ms; 5,376 KB
testcase_11	AC	0 ms; 5,376 KB
testcase_12	AC	0 ms; 5,376 KB
testcase_13	AC	0 ms; 5,376 KB
testcase_14	AC	1 ms; 5,376 KB
testcase_15	AC	1 ms; 5,376 KB
testcase_16	AC	1 ms; 5,376 KB
testcase_17	AC	1 ms; 5,376 KB
testcase_18	AC	1 ms; 5,376 KB
testcase_19	AC	1 ms; 5,376 KB
testcase_20	AC	1 ms; 5,376 KB
testcase_21	AC	1 ms; 5,376 KB
testcase_22	AC	60 ms; 5,376 KB
testcase_23	AC	60 ms; 5,376 KB
testcase_24	AC	1 ms; 5,376 KB
testcase_25	AC	1 ms; 5,376 KB
testcase_26	AC	18 ms; 5,376 KB
testcase_27	AC	1 ms; 5,376 KB
testcase_28	AC	64 ms; 5,376 KB
testcase_29	AC	1 ms; 5,376 KB

コンパイルメッセージ

warning: unused import: `std::io::Write`
  --> src/main.rs:18:5
   |
18 | use std::io::Write;
   |     ^^^^^^^^^^^^^^
   |
   = note: `#[warn(unused_imports)]` on by default

warning: type alias `Map` is never used
  --> src/main.rs:21:6
   |
21 | type Map<K, V> = BTreeMap<K, V>;
   |      ^^^
   |
   = note: `#[warn(dead_code)]` on by default

warning: type alias `Set` is never used
  --> src/main.rs:22:6
   |
22 | type Set<T> = BTreeSet<T>;
   |      ^^^

warning: type alias `Deque` is never used
  --> src/main.rs:23:6
   |
23 | type Deque<T> = VecDeque<T>;
   |      ^^^^^

ソースコード

// 商を計算したい感
// 1 <= i <= N, 1 <= j <= M
// i/j >= q
// なる数を計算したい？
//
// N について商列挙すると？
// l, r, q
// l <= d <= r で floor(n/d) = q
//
// sum_{l <= j <= r} sum_{1 <= i <= N} floor(i/j) * j
// i < qj について
// sum_j sum_{1 <= i < qj} ..
// = sum_j (q-1)q/2 * j
// qj <= i について
// sum_j sum_i qj
// sum_j (N - qj + 1) * q * j

use std::io::Write;
use std::collections::*;

type Map<K, V> = BTreeMap<K, V>;
type Set<T> = BTreeSet<T>;
type Deque<T> = VecDeque<T>;

fn main() {
    input! {
        n: u64,
        m: u64,
    }
    let f = |n: u64| -> M {
        M::from(n) * M::from(n + 1) * M::new(2).inv()
    };
    let g = |n: u64| -> M {
        M::from(n) * M::from(n + 1) * M::from(2 * n + 1) * M::new(6).inv()
    };
    let mut ans = f(n) * M::from(m);
    quot_range_unorderd(n, |l, r, q| {
        if m < l {
            return;
        }
        let r = r.min(m);
        ans -= f(q - 1) * (g(r) - g(l - 1));
        ans -= M::from(n + 1) * M::from(q) * (f(r) - f(l - 1));
        ans += M::from(q) * M::from(q) * (g(r) - g(l - 1));
    });
    println!("{}", ans);
}

// ---------- begin input macro ----------
// reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[macro_export]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

#[macro_export]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[macro_export]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    ($iter:expr, bytes) => {
        read_value!($iter, String).bytes().collect::<Vec<u8>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}
// ---------- end input macro ----------
// ---------- begin modint ----------
use std::marker::*;
use std::ops::*;

pub trait Modulo {
    fn modulo() -> u32;
}

pub struct ConstantModulo<const M: u32>;

impl<const M: u32> Modulo for ConstantModulo<{ M }> {
    fn modulo() -> u32 {
        M
    }
}

pub struct ModInt<T>(u32, PhantomData<T>);

impl<T> Clone for ModInt<T> {
    fn clone(&self) -> Self {
        Self::new_unchecked(self.0)
    }
}

impl<T> Copy for ModInt<T> {}

impl<T: Modulo> Add for ModInt<T> {
    type Output = ModInt<T>;
    fn add(self, rhs: Self) -> Self::Output {
        let mut v = self.0 + rhs.0;
        if v >= T::modulo() {
            v -= T::modulo();
        }
        Self::new_unchecked(v)
    }
}

impl<T: Modulo> AddAssign for ModInt<T> {
    fn add_assign(&mut self, rhs: Self) {
        *self = *self + rhs;
    }
}

impl<T: Modulo> Sub for ModInt<T> {
    type Output = ModInt<T>;
    fn sub(self, rhs: Self) -> Self::Output {
        let mut v = self.0 - rhs.0;
        if self.0 < rhs.0 {
            v += T::modulo();
        }
        Self::new_unchecked(v)
    }
}

impl<T: Modulo> SubAssign for ModInt<T> {
    fn sub_assign(&mut self, rhs: Self) {
        *self = *self - rhs;
    }
}

impl<T: Modulo> Mul for ModInt<T> {
    type Output = ModInt<T>;
    fn mul(self, rhs: Self) -> Self::Output {
        let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64;
        Self::new_unchecked(v as u32)
    }
}

impl<T: Modulo> MulAssign for ModInt<T> {
    fn mul_assign(&mut self, rhs: Self) {
        *self = *self * rhs;
    }
}

impl<T: Modulo> Neg for ModInt<T> {
    type Output = ModInt<T>;
    fn neg(self) -> Self::Output {
        if self.is_zero() {
            Self::zero()
        } else {
            Self::new_unchecked(T::modulo() - self.0)
        }
    }
}

impl<T> std::fmt::Display for ModInt<T> {
    fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

impl<T> std::fmt::Debug for ModInt<T> {
    fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

impl<T> Default for ModInt<T> {
    fn default() -> Self {
        Self::zero()
    }
}

impl<T: Modulo> std::str::FromStr for ModInt<T> {
    type Err = std::num::ParseIntError;
    fn from_str(s: &str) -> Result<Self, Self::Err> {
        let val = s.parse::<u32>()?;
        Ok(ModInt::new(val))
    }
}

impl<T: Modulo> From<usize> for ModInt<T> {
    fn from(val: usize) -> ModInt<T> {
        ModInt::new_unchecked((val % T::modulo() as usize) as u32)
    }
}

impl<T: Modulo> From<u64> for ModInt<T> {
    fn from(val: u64) -> ModInt<T> {
        ModInt::new_unchecked((val % T::modulo() as u64) as u32)
    }
}

impl<T: Modulo> From<i64> for ModInt<T> {
    fn from(val: i64) -> ModInt<T> {
        let mut v = ((val % T::modulo() as i64) + T::modulo() as i64) as u32;
        if v >= T::modulo() {
            v -= T::modulo();
        }
        ModInt::new_unchecked(v)
    }
}

impl<T> ModInt<T> {
    pub fn new_unchecked(n: u32) -> Self {
        ModInt(n, PhantomData)
    }
    pub fn zero() -> Self {
        ModInt::new_unchecked(0)
    }
    pub fn one() -> Self {
        ModInt::new_unchecked(1)
    }
    pub fn is_zero(&self) -> bool {
        self.0 == 0
    }
}

impl<T: Modulo> ModInt<T> {
    pub fn new(d: u32) -> Self {
        ModInt::new_unchecked(d % T::modulo())
    }
    pub fn pow(&self, mut n: u64) -> Self {
        let mut t = Self::one();
        let mut s = *self;
        while n > 0 {
            if n & 1 == 1 {
                t *= s;
            }
            s *= s;
            n >>= 1;
        }
        t
    }
    pub fn inv(&self) -> Self {
        assert!(!self.is_zero());
        self.pow(T::modulo() as u64 - 2)
    }
    pub fn fact(n: usize) -> Self {
        (1..=n).fold(Self::one(), |s, a| s * Self::from(a))
    }
    pub fn perm(n: usize, k: usize) -> Self {
        if k > n {
            return Self::zero();
        }
        ((n - k + 1)..=n).fold(Self::one(), |s, a| s * Self::from(a))
    }
    pub fn binom(n: usize, k: usize) -> Self {
        if k > n {
            return Self::zero();
        }
        let k = k.min(n - k);
        let mut nu = Self::one();
        let mut de = Self::one();
        for i in 0..k {
            nu *= Self::from(n - i);
            de *= Self::from(i + 1);
        }
        nu * de.inv()
    }
}
// ---------- end modint ----------
// ---------- begin precalc ----------
pub struct Precalc<T> {
    fact: Vec<ModInt<T>>,
    ifact: Vec<ModInt<T>>,
    inv: Vec<ModInt<T>>,
}

impl<T: Modulo> Precalc<T> {
    pub fn new(n: usize) -> Precalc<T> {
        let mut inv = vec![ModInt::one(); n + 1];
        let mut fact = vec![ModInt::one(); n + 1];
        let mut ifact = vec![ModInt::one(); n + 1];
        for i in 2..=n {
            fact[i] = fact[i - 1] * ModInt::new_unchecked(i as u32);
        }
        ifact[n] = fact[n].inv();
        if n > 0 {
            inv[n] = ifact[n] * fact[n - 1];
        }
        for i in (1..n).rev() {
            ifact[i] = ifact[i + 1] * ModInt::new_unchecked((i + 1) as u32);
            inv[i] = ifact[i] * fact[i - 1];
        }
        Precalc { fact, ifact, inv }
    }
    pub fn inv(&self, n: usize) -> ModInt<T> {
        assert!(n > 0);
        self.inv[n]
    }
    pub fn fact(&self, n: usize) -> ModInt<T> {
        self.fact[n]
    }
    pub fn ifact(&self, n: usize) -> ModInt<T> {
        self.ifact[n]
    }
    pub fn perm(&self, n: usize, k: usize) -> ModInt<T> {
        if k > n {
            return ModInt::zero();
        }
        self.fact[n] * self.ifact[n - k]
    }
    pub fn binom(&self, n: usize, k: usize) -> ModInt<T> {
        if k > n {
            return ModInt::zero();
        }
        self.fact[n] * self.ifact[k] * self.ifact[n - k]
    }
}
// ---------- end precalc ----------

type M = ModInt<ConstantModulo<998_244_353>>;

// ---------- begin floor sum ----------
// sum_{i = 0}^{n - 1} floor((ai + b) / m)
pub fn floor_sum(n: u64, m: u64, mut a: u64, mut b: u64) -> u64 {
    assert!(n <= 10u64.pow(9));
    assert!(1 <= m && m <= 10u64.pow(9));
    let mut ans = 0;
    ans += a / m * n * (n - 1) / 2 + b / m * n;
    a %= m;
    b %= m;
    let p = a * n + b;
    if p >= m {
        ans += floor_sum(p / m, a, m, p % m);
    }
    ans
}
// ---------- end floor sum ----------
// ---------- begin quot_range ----------
// 商列挙
// n を与えると [1, n] を (l, r, q) な組に分解する
// (l, r, q): x \in [l, r] <=> floor(n / x) = q
//
// 実装が3通りある
// quot_range_orderd
//  (l, r, q) を (1, 1, n), (2, 2, n / 2)... の順に返す
//  除算 ceil(sqrt(n)) 回
//  メモリ O(sqrt(n))
//
// quot_range_unorderd
//  (l, r, q) を (1, 1, n), (ceil(n/2), n, 1), ...の順に返す
//  除算 ceil(sqrt(n)) 回
//  メモリO(1)
//
// quot_range_nanka
//  (l, r, q) を (1, 1, n), (2, 2, n / 2)... の順に返す
//  除算 2 * ceil(sqrt(n)) 回
//  メモリ O(1)
//
// どれがいいかはよくわからない
// 順序不定でいいならunorderd
// 除算が極めて重いならorderd
// ML が気になるならnanka
//
// todo: u32 だけじゃなくu64 でも
#[allow(dead_code)]
pub fn quot_range_orderd<F>(n: u32, mut f: F)
where
    F: FnMut(u32, u32, u32),
{
    let mut p = Vec::with_capacity((n as f64).sqrt().ceil() as usize + 1);
    for d in 1.. {
        let q = n / d;
        p.push((d, q));
        if q < d {
            break;
        }
        f(d, d, q);
        if q == d {
            break;
        }
    }
    for p in p.windows(2).rev() {
        let (l, r, q) = (p[1].1 + 1, p[0].1, p[0].0);
        f(l, r, q);
    }
}

#[allow(dead_code)]
pub fn quot_range_unorderd<F>(n: u64, mut f: F)
where
    F: FnMut(u64, u64, u64)
{
    let mut pre = (0, 0);
    for d in 1.. {
        let q = n / d;
        if pre != (0, 0) {
            let (q, l, r) = (pre.0, q + 1, pre.1);
            f(l, r, q);
        }
        if q < d {
            break;
        }
        pre = (d, q);
        f(d, d, q);
        if q == d {
            break;
        }
    }
}

#[allow(dead_code)]
pub fn quot_range_nanka<F>(n: u32, mut f: F)
where
    F: FnMut(u32, u32, u32)
{
    let mut l = 1;
    while l * l <= n {
        let q = n / l;
        f(l, l, q);
        l += 1;
    }
    let mut q = n / l;
    while q > 0 {
        let r = n / q;
        f(l, r, q);
        l = r + 1;
        q -= 1;
    }
}
// ---------- begin quot_range ----------