結果
問題 | No.1554 array_and_me |
ユーザー |
![]() |
提出日時 | 2021-06-18 22:41:28 |
言語 | Rust (1.83.0 + proconio) |
結果 |
AC
|
実行時間 | 53 ms / 2,000 ms |
コード長 | 9,225 bytes |
コンパイル時間 | 12,643 ms |
コンパイル使用メモリ | 378,680 KB |
実行使用メモリ | 8,576 KB |
最終ジャッジ日時 | 2024-06-22 21:04:48 |
合計ジャッジ時間 | 15,304 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 1 |
other | AC * 41 |
ソースコード
// ---------- begin ModInt ----------mod modint {#[allow(dead_code)]pub struct Mod;impl ConstantModulo for Mod {const MOD: u32 = 998_244_353;}#[allow(dead_code)]pub struct StaticMod;static mut STATIC_MOD: u32 = 0;impl Modulo for StaticMod {fn modulo() -> u32 {unsafe { STATIC_MOD }}}#[allow(dead_code)]impl StaticMod {pub fn set_modulo(p: u32) {unsafe {STATIC_MOD = p;}}}use std::marker::*;use std::ops::*;pub trait Modulo {fn modulo() -> u32;}pub trait ConstantModulo {const MOD: u32;}impl<T> Modulo for TwhereT: ConstantModulo,{fn modulo() -> u32 {T::MOD}}pub struct ModInt<T>(pub u32, PhantomData<T>);impl<T> Clone for ModInt<T> {fn clone(&self) -> Self {ModInt::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 d = self.0 + rhs.0;if d >= T::modulo() {d -= T::modulo();}ModInt::new_unchecked(d)}}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 d = T::modulo() + self.0 - rhs.0;if d >= T::modulo() {d -= T::modulo();}ModInt::new_unchecked(d)}}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;ModInt::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.0 == 0 {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: 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 m = T::modulo() as i64;ModInt::new((val % m + m) as u32)}}#[allow(dead_code)]impl<T> ModInt<T> {pub fn new_unchecked(d: u32) -> Self {ModInt(d, 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}}#[allow(dead_code)]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.0 != 0);self.pow(T::modulo() as u64 - 2)}}}// ---------- end ModInt ----------// ---------- begin Precalc ----------mod precalc {use super::modint::*;#[allow(dead_code)]pub struct Precalc<T> {inv: Vec<ModInt<T>>,fact: Vec<ModInt<T>>,ifact: Vec<ModInt<T>>,}#[allow(dead_code)]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 + 1) {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 {inv: inv,fact: fact,ifact: ifact,}}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 comb(&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 ----------use modint::*;type M = ModInt<Mod>;// ---------- begin scannner ----------#[allow(dead_code)]mod scanner {use std::str::FromStr;pub struct Scanner<'a> {it: std::str::SplitWhitespace<'a>,}impl<'a> Scanner<'a> {pub fn new(s: &'a String) -> Scanner<'a> {Scanner {it: s.split_whitespace(),}}pub fn next<T: FromStr>(&mut self) -> T {self.it.next().unwrap().parse::<T>().ok().unwrap()}pub fn next_bytes(&mut self) -> Vec<u8> {self.it.next().unwrap().bytes().collect()}pub fn next_chars(&mut self) -> Vec<char> {self.it.next().unwrap().chars().collect()}pub fn next_vec<T: FromStr>(&mut self, len: usize) -> Vec<T> {(0..len).map(|_| self.next()).collect()}}}// ---------- end scannner ----------use std::io::Write;fn main() {use std::io::Read;let mut s = String::new();std::io::stdin().read_to_string(&mut s).unwrap();let mut sc = scanner::Scanner::new(&s);let out = std::io::stdout();let mut out = std::io::BufWriter::new(out.lock());run(&mut sc, &mut out);}// sum A_i = S// p_i = A_i / S// (1 + p_i / 1! * x + p_i^2 / 2! * x^2 + ...)#[derive(Clone, Copy, Eq, PartialEq, Debug)]struct Frac {nu: usize,de: usize,}use std::cmp::*;impl Ord for Frac {fn cmp(&self, rhs: &Self) -> Ordering {(self.nu * rhs.de).cmp(&(self.de * rhs.nu))}}impl PartialOrd for Frac {fn partial_cmp(&self, rhs: &Self) -> Option<Ordering> {Some(self.cmp(rhs))}}impl Frac {fn new(nu: usize, de: usize) -> Self {Frac {nu,de,}}}fn run<W: Write>(sc: &mut scanner::Scanner, out: &mut std::io::BufWriter<W>) {let t: u32 = sc.next();for _ in 0..t {let n: usize = sc.next();let k: usize = sc.next();let a: Vec<usize> = sc.next_vec(n);let s = a.iter().sum::<usize>();let mut cnt = vec![0; n];let mut h = std::collections::BinaryHeap::new();for (i, a) in a.iter().enumerate() {h.push((Frac::new(*a, 1), i));}for _ in 0..k {let (_, k) = h.pop().unwrap();cnt[k] += 1;h.push((Frac::new(a[k], cnt[k] + 1), k));}let pc = precalc::Precalc::new(n + k);let mut ans = pc.fact(k);for i in 0..n {ans *= (M::from(a[i]) * M::from(s).inv()).pow(cnt[i] as u64) * pc.ifact(cnt[i]);}writeln!(out, "{}", ans).ok();}}