#567905 (Rust) No.1260 たくさんの多項式

• 問題: No.1260 たくさんの多項式
• ユーザー: akakimidori
• 提出日時: 2020-10-16 22:40:16
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 178 ms / 2,000 ms
• コード長: 8,768 bytes
• コンパイル時間: 11,756 ms
• コンパイル使用メモリ: 377,868 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-07-20 22:57:45
• 合計ジャッジ時間: 17,982 ms
• ジャッジサーバーID （参考情報）: judge3 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	1 ms; 5,376 KB
testcase_04	AC	1 ms; 5,376 KB
testcase_05	AC	3 ms; 5,376 KB
testcase_06	AC	1 ms; 5,376 KB
testcase_07	AC	3 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	2 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	3 ms; 5,376 KB
testcase_15	AC	2 ms; 5,376 KB
testcase_16	AC	1 ms; 5,376 KB
testcase_17	AC	2 ms; 5,376 KB
testcase_18	AC	3 ms; 5,376 KB
testcase_19	AC	2 ms; 5,376 KB
testcase_20	AC	176 ms; 5,376 KB
testcase_21	AC	48 ms; 5,376 KB
testcase_22	AC	145 ms; 5,376 KB
testcase_23	AC	118 ms; 5,376 KB
testcase_24	AC	123 ms; 5,376 KB
testcase_25	AC	96 ms; 5,376 KB
testcase_26	AC	118 ms; 5,376 KB
testcase_27	AC	100 ms; 5,376 KB
testcase_28	AC	168 ms; 5,376 KB
testcase_29	AC	119 ms; 5,376 KB
testcase_30	AC	75 ms; 5,376 KB
testcase_31	AC	120 ms; 5,376 KB
testcase_32	AC	120 ms; 5,376 KB
testcase_33	AC	98 ms; 5,376 KB
testcase_34	AC	166 ms; 5,376 KB
testcase_35	AC	71 ms; 5,376 KB
testcase_36	AC	69 ms; 5,376 KB
testcase_37	AC	123 ms; 5,376 KB
testcase_38	AC	131 ms; 5,376 KB
testcase_39	AC	160 ms; 5,376 KB
testcase_40	AC	120 ms; 5,376 KB
testcase_41	AC	150 ms; 5,376 KB
testcase_42	AC	112 ms; 5,376 KB
testcase_43	AC	156 ms; 5,376 KB
testcase_44	AC	101 ms; 5,376 KB
testcase_45	AC	95 ms; 5,376 KB
testcase_46	AC	89 ms; 5,376 KB
testcase_47	AC	110 ms; 5,376 KB
testcase_48	AC	23 ms; 5,376 KB
testcase_49	AC	83 ms; 5,376 KB
testcase_50	AC	43 ms; 5,376 KB
testcase_51	AC	164 ms; 5,376 KB
testcase_52	AC	56 ms; 5,376 KB
testcase_53	AC	73 ms; 5,376 KB
testcase_54	AC	164 ms; 5,376 KB
testcase_55	AC	178 ms; 5,376 KB
testcase_56	AC	77 ms; 5,376 KB
testcase_57	AC	114 ms; 5,376 KB
testcase_58	AC	70 ms; 5,376 KB
testcase_59	AC	121 ms; 5,376 KB
testcase_60	AC	168 ms; 5,376 KB

ソースコード

// ---------- 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 = T::modulo() + 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: 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)
        }
    }

    #[allow(dead_code)]
    pub fn mod_pow(r: u64, mut n: u64, m: u64) -> u64 {
        let mut t = 1 % m;
        let mut s = r % m;
        while n > 0 {
            if n & 1 == 1 {
                t = t * s % m;
            }
            s = s * s % m;
            n >>= 1;
        }
        t
    }
}
// ---------- 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 ----------
// ---------- 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 modint::*;
type M = ModInt<Mod>;

fn run() {
    input! {
        n: usize,
    }
    let mut ans = M::zero();
    let mut l = n;
    for j in 1usize.. {
        if (j + 1).pow(2) >= n {
            break;
        }
        l = n / (j + 1);
        let r = M::from(n / j);
        let l = M::from(n / (j + 1));
        ans += M::from(j) * (r - l);
        ans += M::from(n) * (r - l) - M::from(j) * (r * (r + M::one()) - l * (l + M::one())) * M::new(2).inv();
    }
    for i in 2..=l {
        let mut n = n;
        while n > 0 {
            ans += M::from(n % i);
            n /= i;
        }
    }
    println!("{}", ans);
}

fn main() {
    run();
}