結果

問題 No.8046 yukicoderの過去問
コンテスト
ユーザー akakimidori
提出日時 2019-10-15 02:37:03
言語 Rust
(1.83.0 + proconio)
結果
TLE  
実行時間 -
コード長 5,779 bytes
コンパイル時間 16,259 ms
コンパイル使用メモリ 378,988 KB
実行使用メモリ 9,704 KB
最終ジャッジ日時 2024-12-25 17:19:03
合計ジャッジ時間 25,182 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
other AC * 4 TLE * 5
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 # 

// ---------- 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 ----------
use std::io::Read;

fn karatsuba(c: &mut [ModInt], a: &[ModInt], b: &[ModInt]) {
    assert!(a.len() == b.len());
    assert!(c.len() == 2 * a.len());
    if a.len() < 64 {
        for (i, a) in a.iter().enumerate() {
            for (c, b) in c[i..].iter_mut().zip(b.iter()) {
                *c += *a * *b;
            }
        }
        return;
    }
    if a.len() & 1 == 1 {
        karatsuba(&mut c[2..], &a[1..], &b[1..]);
        let x = a[0];
        let y = b[0];
        c[0] += x * y;
        for (c, (a, b)) in c[1..].iter_mut().zip(a[1..].iter().zip(b[1..].iter())) {
            *c += x * *b + *a * y;
        }
        return;
    }
    let n = a.len();
    let m = n / 2;
    karatsuba(&mut c[..n], &a[..m], &b[..m]);
    karatsuba(&mut c[n..], &a[m..], &b[m..]);
    let mut x = vec![ModInt::zero(); 2 * n];
    let mut y = x.split_off(m);
    let mut z = y.split_off(m);
    for (x, (a, b)) in x.iter_mut().zip(a.iter().zip(a[m..].iter())) {
        *x = *a + *b;
    }
    for (y, (a, b)) in y.iter_mut().zip(b.iter().zip(b[m..].iter())) {
        *y = *a + *b;
    }
    karatsuba(&mut z, &x, &y);
    for (z, (a, b)) in z.iter_mut().zip(c.iter().zip(c[n..].iter())) {
        *z -= *a + *b;
    }
    for (c, z) in c[m..].iter_mut().zip(z.iter()) {
        *c += *z;
    }
}

fn inverse(a: &Vec<ModInt>, n: usize) -> Vec<ModInt> {
    assert!(a[0].0 > 0);
    let mut b = vec![a[0].inv(); 1];
    let mut k = 1;
    while k < n {
        k *= 2;
        let mut c = vec![ModInt::zero(); k];
        karatsuba(&mut c, &b, &b);
        let mut x = a.clone();
        x.resize(k, ModInt::zero());
        let mut y = vec![ModInt::zero(); 2 * k];
        karatsuba(&mut y, &x, &c);
        b.resize(k, ModInt::zero());
        for (b, y) in b.iter_mut().zip(y.iter()) {
            *b = *b + *b - *y;
        }
    }
    b
}

fn run() {
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();
    let mut it = s.trim().split_whitespace();
    let k: usize = it.next().unwrap().parse().unwrap();
    let n: usize = it.next().unwrap().parse().unwrap();
    let mut a = vec![ModInt::zero(); 100_000 + 1];
    a[0] = ModInt::one();
    for _ in 0..n {
        let x: usize = it.next().unwrap().parse().unwrap();
        a[x] = -ModInt::one();
    }
    let inv = inverse(&a, k + 1);
    println!("{}", inv[k].0);
}

fn main() {
    run();
}
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