結果

問題 No.1847 Good Sequence
ユーザー akakimidoriakakimidori
提出日時 2022-02-18 22:43:53
言語 Rust
(1.77.0)
結果
AC  
実行時間 64 ms / 3,000 ms
コード長 10,259 bytes
コンパイル時間 5,486 ms
コンパイル使用メモリ 191,612 KB
実行使用メモリ 4,388 KB
最終ジャッジ日時 2023-09-11 19:44:17
合計ジャッジ時間 6,662 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge15
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 4 ms
4,380 KB
testcase_01 AC 59 ms
4,384 KB
testcase_02 AC 29 ms
4,380 KB
testcase_03 AC 7 ms
4,384 KB
testcase_04 AC 6 ms
4,384 KB
testcase_05 AC 5 ms
4,380 KB
testcase_06 AC 5 ms
4,384 KB
testcase_07 AC 5 ms
4,380 KB
testcase_08 AC 5 ms
4,380 KB
testcase_09 AC 5 ms
4,384 KB
testcase_10 AC 14 ms
4,384 KB
testcase_11 AC 10 ms
4,384 KB
testcase_12 AC 15 ms
4,380 KB
testcase_13 AC 12 ms
4,384 KB
testcase_14 AC 15 ms
4,384 KB
testcase_15 AC 14 ms
4,384 KB
testcase_16 AC 14 ms
4,384 KB
testcase_17 AC 15 ms
4,380 KB
testcase_18 AC 13 ms
4,380 KB
testcase_19 AC 14 ms
4,388 KB
testcase_20 AC 58 ms
4,384 KB
testcase_21 AC 58 ms
4,380 KB
testcase_22 AC 64 ms
4,380 KB
testcase_23 AC 52 ms
4,384 KB
testcase_24 AC 57 ms
4,384 KB
testcase_25 AC 58 ms
4,384 KB
testcase_26 AC 57 ms
4,380 KB
testcase_27 AC 59 ms
4,380 KB
testcase_28 AC 59 ms
4,380 KB
testcase_29 AC 57 ms
4,380 KB
testcase_30 AC 59 ms
4,380 KB
testcase_31 AC 63 ms
4,384 KB
testcase_32 AC 58 ms
4,384 KB
testcase_33 AC 58 ms
4,384 KB
testcase_34 AC 62 ms
4,380 KB
testcase_35 AC 58 ms
4,380 KB
testcase_36 AC 61 ms
4,380 KB
testcase_37 AC 58 ms
4,384 KB
testcase_38 AC 2 ms
4,380 KB
testcase_39 AC 3 ms
4,380 KB
testcase_40 AC 56 ms
4,380 KB
権限があれば一括ダウンロードができます
コンパイルメッセージ
warning: unused import: `std::io::Write`
   --> Main.rs:307:5
    |
307 | use std::io::Write;
    |     ^^^^^^^^^^^^^^
    |
    = note: `#[warn(unused_imports)]` on by default

warning: type alias `Map` is never used
   --> Main.rs:310:6
    |
310 | type Map<K, V> = BTreeMap<K, V>;
    |      ^^^
    |
    = note: `#[warn(dead_code)]` on by default

warning: type alias `Set` is never used
   --> Main.rs:311:6
    |
311 | type Set<T> = BTreeSet<T>;
    |      ^^^

warning: type alias `Deque` is never used
   --> Main.rs:312:6
    |
312 | type Deque<T> = VecDeque<T>;
    |      ^^^^^

warning: 4 warnings emitted

ソースコード

diff # 

// ---------- begin ModInt ----------
mod modint {

    #[allow(dead_code)]
    pub struct Mod;
    impl ConstantModulo for Mod {
        const MOD: u32 = 1_000_000_007;
    }

    #[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 T
    where
        T: 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 = 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 input macro ----------
// reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    ($iter:expr, bytes) => {
        read_value!($iter, String).bytes().collect::<Vec<u8>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}
// ---------- end input macro ----------

use std::io::Write;
use std::collections::*;

type Map<K, V> = BTreeMap<K, V>;
type Set<T> = BTreeSet<T>;
type Deque<T> = VecDeque<T>;

const SIZE: usize = 70;

type Mat = [[M; SIZE]; SIZE];

fn run() {
    input! {
        l: u64,
        n: usize,
        m: usize,
        k: [usize; m],
    }
    let mut elem = [false; 11];
    for k in k {
        elem[k] = true;
    }
    let mut v = vec![vec![]; 11];
    let mut id = 1;
    for i in 1..=10 {
        for _ in 0..=i {
            v[i].push(id);
            id += 1;
        }
    }
    let ok = id;
    let mut trans = [[M::zero(); SIZE]; SIZE];
    for i in 1..=n {
        if !elem[i] {
            trans[0][0] += M::one();
        } else {
            trans[0][v[i][0]] += M::one();
        }
    }
    for i in 1..=n {
        if !elem[i] {
            continue;
        }
        for j in 0..=i {
            let trans = &mut trans[v[i][j]];
            for x in 1..=n {
                if x != i {
                    if j + 1 == i {
                        trans[ok] += M::one();
                    } else if elem[x] {
                        trans[v[x][0]] += M::one();
                    } else {
                        trans[0] += M::one();
                    }
                } else {
                    let mut j = j + 1;
                    if j > i {
                        j -= 1;
                    }
                    trans[v[i][j]] += M::one();
                }
            }
        }
    }
    trans[ok][ok] += M::from(n);
    let mul = |a: &Mat, b: &Mat| -> Mat {
        let mut c = [[M::zero(); SIZE]; SIZE];
        for (c, a) in c.iter_mut().zip(a) {
            for (a, b) in a.iter().zip(b) {
                for (c, b) in c.iter_mut().zip(b) {
                    *c += *a * *b;
                }
            }
        }
        c
    };
    let mut t = [[M::zero(); SIZE]; SIZE];
    for i in 0..t.len() {
        t[i][i] = M::one();
    }
    let mut r = trans;
    let mut l = l;
    while l > 0 {
        if l & 1 == 1 {
            t = mul(&t, &r);
        }
        r = mul(&r, &r);
        l >>= 1;
    }
    let mut ans = t[0][ok];
    for i in 1..=n {
        ans += t[0][v[i][i - 1]];
    }
    println!("{}", ans);
}

fn main() {
    run();
}
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