結果

問題 No.980 Fibonacci Convolution Hard
ユーザー akakimidori
提出日時 2020-01-31 22:30:09
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 63 ms / 2,000 ms
コード長 5,359 bytes
コンパイル時間 21,537 ms
コンパイル使用メモリ 383,468 KB
実行使用メモリ 11,356 KB
最終ジャッジ日時 2024-09-17 11:33:18
合計ジャッジ時間 24,907 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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 * 17
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<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

impl std::str::FromStr for ModInt {
    type Err = std::num::ParseIntError;
    fn from_str(s: &str) -> Result<Self, Self::Err> {
        let val = s.parse::<u32>()?;
        Ok(ModInt::new(val))
    }
}

#[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 {
        assert!(self.0 > 0);
        self.pow(MOD - 2)
    }
}
// ---------- end ModInt ----------
// ---------- begin Matrix ----------
#[allow(dead_code)]
mod matrix {
    use std::ops::{Add, Mul};
    pub trait SemiRing: Add<Output = Self> + Mul<Output = Self> + Copy {
        fn zero() -> Self;
        fn one() -> Self;
    }
    pub const SIZE: usize = 2;
    #[derive(Clone)]
    pub struct SquareMatrix<T: SemiRing> {
        buf: [[T; SIZE]; SIZE],
    }
    impl<T: SemiRing> SquareMatrix<T> {
        pub fn zero() -> Self {
            let z = T::zero();
            SquareMatrix {
                buf: [[z; SIZE]; SIZE],
            }
        }
        pub fn identity() -> Self {
            let mut m = Self::zero();
            for i in 0..SIZE {
                m.buf[i][i] = T::one();
            }
            m
        }
        pub fn set_at(&mut self, i: usize, j: usize, v: T) {
            self.buf[i][j] = v;
        }
        pub fn get_at(&self, i: usize, j: usize) -> T {
            self.buf[i][j]
        }
        pub fn matmul(&self, rhs: &Self) -> Self {
            let mut res = Self::zero();
            for (x, a) in res.buf.iter_mut().zip(self.buf.iter()) {
                for (a, b) in a.iter().zip(rhs.buf.iter()) {
                    for (x, b) in x.iter_mut().zip(b.iter()) {
                        *x = *x + *a * *b;
                    }
                }
            }
            res
        }
        pub fn matadd(&self, rhs: &Self) -> Self {
            let mut c = Self::zero();
            for (c, (a, b)) in c.buf.iter_mut().zip(self.buf.iter().zip(rhs.buf.iter())) {
                for (c, (a, b)) in c.iter_mut().zip(a.iter().zip(b.iter())) {
                    *c = *a + *b;
                }
            }
            c
        }
        pub fn matpow(&self, mut n: usize) -> Self {
            let mut t = Self::identity();
            let mut s = self.clone();
            while n > 0 {
                if n & 1 == 1 {
                    t = t.matmul(&s);
                }
                s = s.matmul(&s);
                n >>= 1;
            }
            t
        }
    }
}
// ---------- end Matrix ----------

use std::io::Read;
use std::io::Write;
use matrix::*;

impl SemiRing for ModInt {
    fn zero() -> Self {
        ModInt::zero()
    }
    fn one() -> Self {
        ModInt::one()
    }
}

fn run() {
    let out = std::io::stdout();
    let mut out = std::io::BufWriter::new(out.lock());
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();
    let mut it = s.trim().split_whitespace();
    let p: ModInt = it.next().unwrap().parse().unwrap();
    let mut r = SquareMatrix::<ModInt>::zero();
    r.set_at(0, 0, p);
    r.set_at(0, 1, ModInt::one());
    r.set_at(1, 0, ModInt::one());
    let r = r;
    let m = 2_000_000;
    let mut f = vec![ModInt::zero(); m + 1];
    f[2] = ModInt::zero();
    f[3] = ModInt::zero();
    let mut a = r.matpow(2);
    for i in 4..=m {
        f[i] = ModInt((i - 3) as u32) * a.get_at(1, 1) - f[i - 2];
        a = a.matmul(&r);
    }
    it.next();
    for s in it {
        let q: usize = s.parse().unwrap();
        writeln!(out, "{}", f[q]).ok();
    }
}

fn main() {
    run();
}
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