結果

問題 No.1259 スイッチ
ユーザー koba-e964koba-e964
提出日時 2021-09-11 17:10:55
言語 Rust
(1.77.0 + proconio)
結果
AC  
実行時間 147 ms / 2,000 ms
コード長 6,673 bytes
コンパイル時間 15,132 ms
コンパイル使用メモリ 378,952 KB
実行使用メモリ 25,216 KB
最終ジャッジ日時 2024-06-23 01:25:38
合計ジャッジ時間 19,866 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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 1 ms
5,248 KB
testcase_01 AC 2 ms
5,248 KB
testcase_02 AC 2 ms
5,248 KB
testcase_03 AC 1 ms
5,248 KB
testcase_04 AC 1 ms
5,376 KB
testcase_05 AC 1 ms
5,376 KB
testcase_06 AC 2 ms
5,376 KB
testcase_07 AC 2 ms
5,376 KB
testcase_08 AC 1 ms
5,376 KB
testcase_09 AC 2 ms
5,376 KB
testcase_10 AC 88 ms
15,872 KB
testcase_11 AC 134 ms
23,680 KB
testcase_12 AC 86 ms
15,104 KB
testcase_13 AC 46 ms
9,728 KB
testcase_14 AC 68 ms
13,056 KB
testcase_15 AC 45 ms
9,472 KB
testcase_16 AC 111 ms
19,968 KB
testcase_17 AC 66 ms
12,672 KB
testcase_18 AC 127 ms
22,400 KB
testcase_19 AC 125 ms
22,144 KB
testcase_20 AC 93 ms
16,128 KB
testcase_21 AC 145 ms
24,320 KB
testcase_22 AC 44 ms
8,576 KB
testcase_23 AC 127 ms
21,760 KB
testcase_24 AC 91 ms
17,152 KB
testcase_25 AC 88 ms
16,384 KB
testcase_26 AC 141 ms
24,704 KB
testcase_27 AC 113 ms
20,352 KB
testcase_28 AC 89 ms
16,640 KB
testcase_29 AC 112 ms
20,352 KB
testcase_30 AC 15 ms
9,344 KB
testcase_31 AC 22 ms
12,928 KB
testcase_32 AC 11 ms
6,400 KB
testcase_33 AC 31 ms
17,152 KB
testcase_34 AC 18 ms
10,112 KB
testcase_35 AC 25 ms
13,568 KB
testcase_36 AC 23 ms
12,544 KB
testcase_37 AC 20 ms
11,904 KB
testcase_38 AC 19 ms
11,136 KB
testcase_39 AC 29 ms
16,384 KB
testcase_40 AC 31 ms
16,512 KB
testcase_41 AC 26 ms
13,952 KB
testcase_42 AC 32 ms
16,896 KB
testcase_43 AC 19 ms
10,496 KB
testcase_44 AC 29 ms
16,000 KB
testcase_45 AC 31 ms
17,408 KB
testcase_46 AC 16 ms
10,240 KB
testcase_47 AC 29 ms
17,280 KB
testcase_48 AC 15 ms
9,216 KB
testcase_49 AC 31 ms
16,768 KB
testcase_50 AC 78 ms
14,336 KB
testcase_51 AC 42 ms
8,704 KB
testcase_52 AC 134 ms
23,808 KB
testcase_53 AC 61 ms
11,392 KB
testcase_54 AC 142 ms
23,552 KB
testcase_55 AC 41 ms
8,320 KB
testcase_56 AC 67 ms
12,800 KB
testcase_57 AC 122 ms
21,760 KB
testcase_58 AC 84 ms
15,488 KB
testcase_59 AC 105 ms
18,688 KB
testcase_60 AC 147 ms
25,216 KB
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 # 

use std::cmp::*;
// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes.by_ref().map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

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

macro_rules! read_value {
    ($next:expr, usize1) => (read_value!($next, usize) - 1);
    ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error"));
}

/// Verified by https://atcoder.jp/contests/arc093/submissions/3968098
mod 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 >= 0
        pub 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, 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_int

macro_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 = 1_000_000_007;
define_mod!(P, MOD);
type MInt = mod_int::ModInt<P>;

// Depends on MInt.rs
fn fact_init(w: usize) -> (Vec<MInt>, Vec<MInt>) {
    let mut fac = vec![MInt::new(1); w];
    let mut invfac = vec![0.into(); w];
    for i in 1 .. w {
        fac[i] = fac[i - 1] * i as i64;
    }
    invfac[w - 1] = fac[w - 1].inv();
    for i in (0 .. w - 1).rev() {
        invfac[i] = invfac[i + 1] * (i as i64 + 1);
    }
    (fac, invfac)
}

fn main() {
    input!(n: usize, k: usize, m: usize1);
    assert_eq!(std::mem::size_of::<usize>(), 8);
    let nn = MInt::new(n as i64);
    let (fac, invfac) = fact_init(n + 1);
    let mut tot = MInt::new(0);
    if m == 0 {
        for per in 1..n + 1 {
            if k % per == 0 {
                tot += fac[n - 1] * invfac[n - per] * nn.pow((n - per) as i64);
            }
        }
    } else {
        for per in 2..n + 1 {
            let r = k % per;
            let tmp = fac[n - 2] * invfac[n - per] * nn.pow((n - per) as i64);
            if r == 0 {
                continue;
            }
            tot += tmp;
        }
        let mut acc = vec![MInt::new(0); n];
        let mut cur = MInt::new(1);
        for i in 0..n - 1 {
            acc[i + 1] = acc[i] + invfac[i] * cur;
            cur *= nn;
        }
        for per in 1..n {
            let hi = min(n - 1 - per, k - 1);
            // tmp = (n - 1 - per)!/(n - 1 - per)! * n^{n - 1 - per} + .. + (n - 1 - per)!/(n - 1 - per - hi)! * n^{n - 1 - per - hi}
            let tmp = fac[n - 1 - per] * (acc[n - per] - acc[n - 1 - per - hi]);
            tot += tmp * fac[n - 2] * invfac[per - 1] * invfac[n - per - 1] * fac[per - 1];
        }
        if k < n {
            for per in 1..n - k {
                // tmp = (n - 2 - per)!/0! * n^{0} + .. + (n - 2 - per)!/(n - 1 - per - k)! * n^{n - 1 - per - k}
                let tmp = fac[n - 2 - per] * acc[n - per - k];
                tot += tmp * fac[n - 2] * invfac[per] * invfac[n - per - 2] * fac[per - 1] * per as i64;
            }
        }
    }
    println!("{}", tot);
}
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