結果

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
(1.83.0 + 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
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 27
権限があれば一括ダウンロードができます
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

diff #
プレゼンテーションモードにする

//
// 1 <= i <= N, 1 <= j <= M
// i/j >= q
//
//
// N
// l, r, q
// l <= d <= r floor(n/d) = q
//
// sum_{l <= j <= r} sum_{1 <= i <= N} floor(i/j) * j
// i < qj
// sum_j sum_{1 <= i < qj} ..
// = sum_j (q-1)q/2 * j
// qj <= i
// 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 ----------
//
// n [1, n] (l, r, q)
// (l, r, q): x \in [l, r] <=> floor(n / x) = q
//
// 3
// quot_range_orderd
// (l, r, q) (1, 1, n), (2, 2, n / 2)...
// ceil(sqrt(n))
// O(sqrt(n))
//
// quot_range_unorderd
// (l, r, q) (1, 1, n), (ceil(n/2), n, 1), ...
// ceil(sqrt(n))
// O(1)
//
// quot_range_nanka
// (l, r, q) (1, 1, n), (2, 2, n / 2)...
// 2 * ceil(sqrt(n))
// O(1)
//
//
// unorderd
// orderd
// ML nanka
//
// todo: u32 u64
#[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 ----------
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