結果
問題 | No.1962 Not Divide |
ユーザー |
|
提出日時 | 2024-04-16 22:30:33 |
言語 | Rust (1.83.0 + proconio) |
結果 |
AC
|
実行時間 | 177 ms / 2,000 ms |
コード長 | 11,190 bytes |
コンパイル時間 | 17,840 ms |
コンパイル使用メモリ | 377,976 KB |
実行使用メモリ | 5,248 KB |
最終ジャッジ日時 | 2024-10-08 04:09:48 |
合計ジャッジ時間 | 17,756 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 21 |
ソースコード
#[allow(unused_imports)]use std::cmp::*;#[allow(unused_imports)]use std::collections::*;use std::io::Read;fn get_word() -> String {let stdin = std::io::stdin();let mut stdin=stdin.lock();let mut u8b: [u8; 1] = [0];loop {let mut buf: Vec<u8> = Vec::with_capacity(16);loop {let res = stdin.read(&mut u8b);if res.unwrap_or(0) == 0 || u8b[0] <= b' ' {break;} else {buf.push(u8b[0]);}}if buf.len() >= 1 {let ret = String::from_utf8(buf).unwrap();return ret;}}}#[allow(dead_code)]fn get<T: std::str::FromStr>() -> T { get_word().parse().ok().unwrap() }/// Verified by https://atcoder.jp/contests/abc198/submissions/21774342mod mod_int {use std::ops::*;pub trait Mod: Copy { fn m() -> i64; }#[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)]pub struct ModInt<M> { pub x: i64, phantom: ::std::marker::PhantomData<M> }impl<M: Mod> ModInt<M> {// x >= 0pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) }fn new_internal(x: i64) -> Self {ModInt { x: x, phantom: ::std::marker::PhantomData }}pub fn pow(self, mut e: i64) -> Self {debug_assert!(e >= 0);let mut sum = ModInt::new_internal(1);let mut cur = self;while e > 0 {if e % 2 != 0 { sum *= cur; }cur *= cur;e /= 2;}sum}#[allow(dead_code)]pub fn inv(self) -> Self { self.pow(M::m() - 2) }}impl<M: Mod> Default for ModInt<M> {fn default() -> Self { Self::new_internal(0) }}impl<M: Mod, T: Into<ModInt<M>>> Add<T> for ModInt<M> {type Output = Self;fn add(self, other: T) -> Self {let other = other.into();let mut sum = self.x + other.x;if sum >= M::m() { sum -= M::m(); }ModInt::new_internal(sum)}}impl<M: Mod, T: Into<ModInt<M>>> Sub<T> for ModInt<M> {type Output = Self;fn sub(self, other: T) -> Self {let other = other.into();let mut sum = self.x - other.x;if sum < 0 { sum += M::m(); }ModInt::new_internal(sum)}}impl<M: Mod, T: Into<ModInt<M>>> Mul<T> for ModInt<M> {type Output = Self;fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) }}impl<M: Mod, T: Into<ModInt<M>>> AddAssign<T> for ModInt<M> {fn add_assign(&mut self, other: T) { *self = *self + other; }}impl<M: Mod, T: Into<ModInt<M>>> SubAssign<T> for ModInt<M> {fn sub_assign(&mut self, other: T) { *self = *self - other; }}impl<M: Mod, T: Into<ModInt<M>>> MulAssign<T> for ModInt<M> {fn mul_assign(&mut self, other: T) { *self = *self * other; }}impl<M: Mod> Neg for ModInt<M> {type Output = Self;fn neg(self) -> Self { ModInt::new(0) - self }}impl<M> ::std::fmt::Display for ModInt<M> {fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {self.x.fmt(f)}}impl<M: Mod> ::std::fmt::Debug for ModInt<M> {fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {let (mut a, mut b, _) = red(self.x, M::m());if b < 0 {a = -a;b = -b;}write!(f, "{}/{}", a, b)}}impl<M: Mod> From<i64> for ModInt<M> {fn from(x: i64) -> Self { Self::new(x) }}// Finds the simplest fraction x/y congruent to r mod p.// The return value (x, y, z) satisfies x = y * r + z * p.fn red(r: i64, p: i64) -> (i64, i64, i64) {if r.abs() <= 10000 {return (r, 1, 0);}let mut nxt_r = p % r;let mut q = p / r;if 2 * nxt_r >= r {nxt_r -= r;q += 1;}if 2 * nxt_r <= -r {nxt_r += r;q -= 1;}let (x, z, y) = red(nxt_r, r);(x, y - q * z, z)}} // mod mod_intmacro_rules! define_mod {($struct_name: ident, $modulo: expr) => {#[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]struct $struct_name {}impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } }}}const MOD: i64 = 998_244_353;define_mod!(P, MOD);type MInt = mod_int::ModInt<P>;// FFT (in-place, verified as NTT only)// R: Ring + Copy// Verified by: https://judge.yosupo.jp/submission/53831// Adopts the technique used in https://judge.yosupo.jp/submission/3153.mod fft {use std::ops::*;// n should be a power of 2. zeta is a primitive n-th root of unity.// one is unity// Note that the result is bit-reversed.pub fn fft<R>(f: &mut [R], zeta: R, one: R)where R: Copy +Add<Output = R> +Sub<Output = R> +Mul<Output = R> {let n = f.len();assert!(n.is_power_of_two());let mut m = n;let mut base = zeta;unsafe {while m > 2 {m >>= 1;let mut r = 0;while r < n {let mut w = one;for s in r..r + m {let &u = f.get_unchecked(s);let d = *f.get_unchecked(s + m);*f.get_unchecked_mut(s) = u + d;*f.get_unchecked_mut(s + m) = w * (u - d);w = w * base;}r += 2 * m;}base = base * base;}if m > 1 {// m = 1let mut r = 0;while r < n {let &u = f.get_unchecked(r);let d = *f.get_unchecked(r + 1);*f.get_unchecked_mut(r) = u + d;*f.get_unchecked_mut(r + 1) = u - d;r += 2;}}}}pub fn inv_fft<R>(f: &mut [R], zeta_inv: R, one: R)where R: Copy +Add<Output = R> +Sub<Output = R> +Mul<Output = R> {let n = f.len();assert!(n.is_power_of_two());let zeta = zeta_inv; // inverse FFTlet mut zetapow = Vec::with_capacity(20);{let mut m = 1;let mut cur = zeta;while m < n {zetapow.push(cur);cur = cur * cur;m *= 2;}}let mut m = 1;unsafe {if m < n {zetapow.pop();let mut r = 0;while r < n {let &u = f.get_unchecked(r);let d = *f.get_unchecked(r + 1);*f.get_unchecked_mut(r) = u + d;*f.get_unchecked_mut(r + 1) = u - d;r += 2;}m = 2;}while m < n {let base = zetapow.pop().unwrap();let mut r = 0;while r < n {let mut w = one;for s in r..r + m {let &u = f.get_unchecked(s);let d = *f.get_unchecked(s + m) * w;*f.get_unchecked_mut(s) = u + d;*f.get_unchecked_mut(s + m) = u - d;w = w * base;}r += 2 * m;}m *= 2;}}}}// Depends on: fft.rs, MInt.rs// Verified by: ABC269-Ex (https://atcoder.jp/contests/abc269/submissions/39116328)pub struct FPSOps<M: mod_int::Mod> {gen: mod_int::ModInt<M>,}impl<M: mod_int::Mod> FPSOps<M> {pub fn new(gen: mod_int::ModInt<M>) -> Self {FPSOps { gen: gen }}}impl<M: mod_int::Mod> FPSOps<M> {pub fn add(&self, mut a: Vec<mod_int::ModInt<M>>, mut b: Vec<mod_int::ModInt<M>>) -> Vec<mod_int::ModInt<M>> {if a.len() < b.len() {std::mem::swap(&mut a, &mut b);}for i in 0..b.len() {a[i] += b[i];}a}pub fn mul(&self, a: Vec<mod_int::ModInt<M>>, b: Vec<mod_int::ModInt<M>>) -> Vec<mod_int::ModInt<M>> {type MInt<M> = mod_int::ModInt<M>;if a.is_empty() || b.is_empty() {return vec![];}let n = a.len() - 1;let m = b.len() - 1;let mut p = 1;while p <= n + m { p *= 2; }let mut f = vec![MInt::new(0); p];let mut g = vec![MInt::new(0); p];for i in 0..n + 1 { f[i] = a[i]; }for i in 0..m + 1 { g[i] = b[i]; }let fac = MInt::new(p as i64).inv();let zeta = self.gen.pow((M::m() - 1) / p as i64);fft::fft(&mut f, zeta, 1.into());fft::fft(&mut g, zeta, 1.into());for i in 0..p { f[i] *= g[i] * fac; }fft::inv_fft(&mut f, zeta.inv(), 1.into());f.truncate(n + m + 1);f}}// Finds [x^n] p(x)/q(x)// Ref: https://qiita.com/ryuhe1/items/da5acbcce4ac1911f47a// Verified by: https://atcoder.jp/contests/tdpc/submissions/24583334// Depends on: MInt.rsfn bostan_mori(ops: &FPSOps<P>, p: &[MInt], q: &[MInt], mut n: i64) -> MInt {if p.is_empty() {return 0.into();}assert!(p.len() < q.len());let mut p = p.to_vec();let mut q = q.to_vec();while n > 0 {let mut qn = q.clone();for i in 0..qn.len() {if i % 2 == 1 {qn[i] = -qn[i];}}let num = ops.mul(p, qn.clone());let den = ops.mul(q.clone(), qn);let mut nxt_p = vec![MInt::new(0); q.len() - 1];let mut nxt_q = vec![MInt::new(0); q.len()];for i in 0..q.len() - 1 {let to = 2 * i + (n % 2) as usize;if to < num.len() {nxt_p[i] = num[to];}}for i in 0..q.len() {nxt_q[i] = den[2 * i];}p = nxt_p;q = nxt_q;n /= 2;}p[0] * q[0].inv()}fn main() {let n: i64 = get();let m: usize = get();let ops = FPSOps::new(MInt::new(3));let mut num = vec![];let mut den = vec![MInt::new(1)];for i in 2..m + 1 {// g += (x+...+x^{i-1}) / (1+...+x^{i-1}-x^i)let mut num1 = vec![MInt::new(1); i];num1[0] -= 1;let mut den1 = vec![MInt::new(1); i + 1];den1[i] -= 2;let newnum = ops.mul(num.clone(), den1.clone());let newnum = ops.add(newnum, ops.mul(den.clone(), num1.clone()));let newden = ops.mul(den.clone(), den1);num = newnum;den = newden;}// g / (1 - g) = num / (den - num)for i in 0..num.len() {den[i] -= num[i];}let ans = bostan_mori(&ops, &num, &den, n);println!("{}", ans);}