結果

問題 No.890 移調の限られた旋法
ユーザー akakimidori
提出日時 2019-09-20 22:01:33
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 22 ms / 2,000 ms
コード長 4,482 bytes
コンパイル時間 19,111 ms
コンパイル使用メモリ 378,548 KB
実行使用メモリ 13,628 KB
最終ジャッジ日時 2024-09-14 17:33:16
合計ジャッジ時間 17,372 ms
ジャッジサーバーID
(参考情報)
judge4 / judge5
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 * 32
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

// ---------- begin ModInt ----------
const MOD: u32 = 1_000_000_007;
#[derive(Clone, Copy)]
struct ModInt(u32);
impl std::ops::Add for ModInt {
type Output = ModInt;
fn add(self, rhs: ModInt) -> Self::Output {
let mut d = self.0 + rhs.0;
if d >= MOD {
d -= MOD;
}
ModInt(d)
}
}
impl std::ops::AddAssign for ModInt {
fn add_assign(&mut self, rhs: ModInt) {
*self = *self + rhs;
}
}
impl std::ops::Sub for ModInt {
type Output = ModInt;
fn sub(self, rhs: ModInt) -> Self::Output {
let mut d = self.0 + MOD - rhs.0;
if d >= MOD {
d -= MOD;
}
ModInt(d)
}
}
impl std::ops::SubAssign for ModInt {
fn sub_assign(&mut self, rhs: ModInt) {
*self = *self - rhs;
}
}
impl std::ops::Mul for ModInt {
type Output = ModInt;
fn mul(self, rhs: ModInt) -> Self::Output {
ModInt((self.0 as u64 * rhs.0 as u64 % MOD as u64) as u32)
}
}
impl std::ops::MulAssign for ModInt {
fn mul_assign(&mut self, rhs: ModInt) {
*self = *self * rhs;
}
}
impl std::ops::Neg for ModInt {
type Output = ModInt;
fn neg(self) -> Self::Output {
ModInt(if self.0 == 0 {0} else {MOD - self.0})
}
}
impl std::fmt::Display for ModInt {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
write!(f, "{}", self.0)
}
}
#[allow(dead_code)]
impl ModInt {
pub fn new(n: u32) -> ModInt {
ModInt(n % MOD)
}
pub fn zero() -> ModInt {
ModInt(0)
}
pub fn one() -> ModInt {
ModInt(1)
}
pub fn pow(self, mut n: u32) -> ModInt {
let mut t = ModInt::one();
let mut s = self;
while n > 0 {
if n & 1 == 1 {
t *= s;
}
s *= s;
n >>= 1;
}
t
}
pub fn inv(self) -> ModInt {
self.pow(MOD - 2)
}
pub fn comb(n: u32, k: u32) -> ModInt {
if k > n {
return ModInt::zero();
}
let k = std::cmp::min(k, n - k);
let mut nu = ModInt::one();
let mut de = ModInt::one();
for i in 0..k {
nu *= ModInt(n - i);
de *= ModInt(i + 1);
}
nu * de.inv()
}
}
#[allow(dead_code)]
struct Precalc {
inv: Vec<ModInt>,
fact: Vec<ModInt>,
ifact: Vec<ModInt>,
}
#[allow(dead_code)]
impl Precalc {
pub fn new(n: usize) -> Precalc {
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) {
inv[i] = -inv[MOD as usize % i] * ModInt(MOD / i as u32);
fact[i] = fact[i - 1] * ModInt(i as u32);
ifact[i] = ifact[i - 1] * inv[i];
}
Precalc {
inv: inv,
fact: fact,
ifact: ifact,
}
}
pub fn inv(&self, n: usize) -> ModInt {
self.inv[n]
}
pub fn fact(&self, n: usize) -> ModInt {
self.fact[n]
}
pub fn ifact(&self, n: usize) -> ModInt {
self.ifact[n]
}
pub fn comb(&self, n: usize, k: usize) -> ModInt {
if k > n {
return ModInt::zero();
}
self.fact[n] * self.ifact[k] * self.ifact[n - k]
}
}
// ---------- end ModInt ----------
fn gcd(a: usize, b: usize) -> usize {
if b == 0 {a} else {gcd(b, a % b)}
}
fn run() {
let mut s = String::new();
std::io::stdin().read_line(&mut s).unwrap();
let mut it = s.trim().split_whitespace();
let n: usize = it.next().unwrap().parse().unwrap();
let k: usize = it.next().unwrap().parse().unwrap();
let mut g = gcd(n, k);
if g == 1 {
println!("0");
return;
}
let mut d = 2;
let mut p = vec![];
while d * d <= g {
if g % d == 0 {
p.push(d);
while g % d == 0 {
g /= d;
}
}
d += 1;
}
if g > 1 {
p.push(g);
}
let pc = Precalc::new(n);
let mut ans = ModInt::zero();
let len = p.len();
for i in 1..(1 << len) {
let mut f = 1;
let mut sign = -ModInt::one();
for j in 0..len {
if (i >> j) & 1 == 1 {
f *= p[j];
sign = -sign;
}
}
ans += sign * pc.comb(n / f, k / f);
}
println!("{}", ans);
}
fn main() {
run();
}
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