結果

問題 No.2613 Sum of Combination
コンテスト
ユーザー koba-e964
提出日時 2024-04-25 20:17:55
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 382 ms / 4,500 ms
コード長 11,074 bytes
コンパイル時間 13,536 ms
コンパイル使用メモリ 379,104 KB
実行使用メモリ 17,920 KB
最終ジャッジ日時 2024-11-08 08:04:06
合計ジャッジ時間 24,529 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 3
other AC * 49
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 # 

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
use std::io::Read;

fn get_word() -> String {
    let stdin = std::io::stdin();
    let mut stdin=stdin.lock();
    let mut u8b: [u8; 1] = [0];
    loop {
        let mut buf: Vec<u8> = Vec::with_capacity(16);
        loop {
            let res = stdin.read(&mut u8b);
            if res.unwrap_or(0) == 0 || u8b[0] <= b' ' {
                break;
            } else {
                buf.push(u8b[0]);
            }
        }
        if buf.len() >= 1 {
            let ret = String::from_utf8(buf).unwrap();
            return ret;
        }
    }
}

fn get<T: std::str::FromStr>() -> T { get_word().parse().ok().unwrap() }

/// Verified by https://atcoder.jp/contests/abc198/submissions/21774342
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> Default for ModInt<M> {
        fn default() -> Self { Self::new_internal(0) }
    }
    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)]
        pub struct $struct_name {}
        impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } }
    }
}
const MOD: i64 = 998_244_353;
define_mod!(P, MOD);
type MInt = mod_int::ModInt<P>;

// FFT (in-place, verified as NTT only)
// R: Ring + Copy
// Verified by: https://judge.yosupo.jp/submission/53831
// Adopts the technique used in https://judge.yosupo.jp/submission/3153.
mod fft {
    use std::ops::*;
    // n should be a power of 2. zeta is a primitive n-th root of unity.
    // one is unity
    // Note that the result is bit-reversed.
    pub fn fft<R>(f: &mut [R], zeta: R, one: R)
        where R: Copy +
        Add<Output = R> +
        Sub<Output = R> +
        Mul<Output = R> {
        let n = f.len();
        assert!(n.is_power_of_two());
        let mut m = n;
        let mut base = zeta;
        unsafe {
            while m > 2 {
                m >>= 1;
                let mut r = 0;
                while r < n {
                    let mut w = one;
                    for s in r..r + m {
                        let &u = f.get_unchecked(s);
                        let d = *f.get_unchecked(s + m);
                        *f.get_unchecked_mut(s) = u + d;
                        *f.get_unchecked_mut(s + m) = w * (u - d);
                        w = w * base;
                    }
                    r += 2 * m;
                }
                base = base * base;
            }
            if m > 1 {
                // m = 1
                let mut r = 0;
                while r < n {
                    let &u = f.get_unchecked(r);
                    let d = *f.get_unchecked(r + 1);
                    *f.get_unchecked_mut(r) = u + d;
                    *f.get_unchecked_mut(r + 1) = u - d;
                    r += 2;
                }
            }
        }
    }
    pub fn inv_fft<R>(f: &mut [R], zeta_inv: R, one: R)
        where R: Copy +
        Add<Output = R> +
        Sub<Output = R> +
        Mul<Output = R> {
        let n = f.len();
        assert!(n.is_power_of_two());
        let zeta = zeta_inv; // inverse FFT
        let mut zetapow = Vec::with_capacity(20);
        {
            let mut m = 1;
            let mut cur = zeta;
            while m < n {
                zetapow.push(cur);
                cur = cur * cur;
                m *= 2;
            }
        }
        let mut m = 1;
        unsafe {
            if m < n {
                zetapow.pop();
                let mut r = 0;
                while r < n {
                    let &u = f.get_unchecked(r);
                    let d = *f.get_unchecked(r + 1);
                    *f.get_unchecked_mut(r) = u + d;
                    *f.get_unchecked_mut(r + 1) = u - d;
                    r += 2;
                }
                m = 2;
            }
            while m < n {
                let base = zetapow.pop().unwrap();
                let mut r = 0;
                while r < n {
                    let mut w = one;
                    for s in r..r + m {
                        let &u = f.get_unchecked(s);
                        let d = *f.get_unchecked(s + m) * w;
                        *f.get_unchecked_mut(s) = u + d;
                        *f.get_unchecked_mut(s + m) = u - d;
                        w = w * base;
                    }
                    r += 2 * m;
                }
                m *= 2;
            }
        }
    }
}

// Depends on: fft.rs, MInt.rs
// Verified by: ABC269-Ex (https://atcoder.jp/contests/abc269/submissions/39116328)
pub struct FPSOps<M: mod_int::Mod> {
    gen: mod_int::ModInt<M>,
}

impl<M: mod_int::Mod> FPSOps<M> {
    pub fn new(gen: mod_int::ModInt<M>) -> Self {
        FPSOps { gen: gen }
    }
}

impl<M: mod_int::Mod> FPSOps<M> {
    pub fn add(&self, mut a: Vec<mod_int::ModInt<M>>, mut b: Vec<mod_int::ModInt<M>>) -> Vec<mod_int::ModInt<M>> {
        if a.len() < b.len() {
            std::mem::swap(&mut a, &mut b);
        }
        for i in 0..b.len() {
            a[i] += b[i];
        }
        a
    }
    pub fn mul(&self, a: Vec<mod_int::ModInt<M>>, b: Vec<mod_int::ModInt<M>>) -> Vec<mod_int::ModInt<M>> {
        type MInt<M> = mod_int::ModInt<M>;
        if a.is_empty() || b.is_empty() {
            return vec![];
        }
        let n = a.len() - 1;
        let m = b.len() - 1;
        let mut p = 1;
        while p <= n + m { p *= 2; }
        let mut f = vec![MInt::new(0); p];
        let mut g = vec![MInt::new(0); p];
        for i in 0..n + 1 { f[i] = a[i]; }
        for i in 0..m + 1 { g[i] = b[i]; }
        let fac = MInt::new(p as i64).inv();
        let zeta = self.gen.pow((M::m() - 1) / p as i64);
        fft::fft(&mut f, zeta, 1.into());
        fft::fft(&mut g, zeta, 1.into());
        for i in 0..p { f[i] *= g[i] * fac; }
        fft::inv_fft(&mut f, zeta.inv(), 1.into());
        f.truncate(n + m + 1);
        f
    }
}

// O(40p)
fn find_generator(p: usize) -> usize {
    fn is_gen(g: usize, p: usize) -> bool {
        let mut cur = g;
        for _ in 1..p - 1 {
            if cur == 1 {
                return false;
            }
            cur = cur * g % p;
        }
        true
    }
    if p == 2 {
        return 1;
    }
    let mut g = 2;
    loop {
        if is_gen(g, p) {
            return g;
        }
        g += 1;
    }
}

// Ref: https://techtipshoge.blogspot.com/2012/04/facebook-hacker-cup-2011-round2-scott.html
// Tags: discrete-logarithm, lucas-theorem, generator-of-finite-fields
fn main() {
    let mut n: i64 = get();
    let p: usize = get();
    let pp = p as i64;
    let mut dig = vec![];
    while n > 0 {
        dig.push((n % pp) as usize);
        n /= pp;
    }
    let g = find_generator(p);
    let mut log = vec![0; p];
    let mut exp = vec![0; p - 1];
    let mut cur = 1;
    for i in 0..p - 1 {
        log[cur] = i;
        exp[i] = cur;
        cur = cur * g % p;
    }
    let mut logfac = vec![0; p];
    for i in 1..p {
        logfac[i] = (logfac[i - 1] + log[i]) % (p - 1);
    }
    let mut cur = vec![MInt::new(0); p - 1];
    cur[0] += 1;
    let ops = FPSOps::new(MInt::new(3));
    for d in dig {
        let mut me = vec![MInt::new(0); p - 1];
        for i in 0..d + 1 {
            let idx = (2 * p - 2 + logfac[d] - logfac[i] - logfac[d - i]) % (p - 1);
            me[idx] += 1;
        }
        let tmp = ops.mul(cur, me);
        cur = vec![MInt::new(0); p - 1];
        cur.copy_from_slice(&tmp[..p - 1]);
        for i in p - 1..2 * p - 3 {
            cur[i - (p - 1)] += tmp[i];
        }
    }
    let mut tot = MInt::new(0);
    for i in 0..p - 1 {
        tot += cur[i] * exp[i] as i64;
    }
    println!("{}", tot);
}
0