#700045 (Rust) No.137 貯金箱の焦り

• 問題: No.137 貯金箱の焦り
• ユーザー: koba-e964
• 提出日時: 2021-09-16 23:55:09
• 言語: Rust (1.77.0 + proconio)
• 結果: TLE
• 実行時間: -
• コード長: 13,814 bytes
• コンパイル時間: 13,329 ms
• コンパイル使用メモリ: 399,056 KB
• 実行使用メモリ: 14,296 KB
• 最終ジャッジ日時: 2024-06-29 17:17:43
• 合計ジャッジ時間: 20,036 ms
• ジャッジサーバーID （参考情報）: judge4 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	15 ms; 6,816 KB
testcase_01	AC	6 ms; 6,812 KB
testcase_02	AC	51 ms; 6,940 KB
testcase_03	AC	1 ms; 6,940 KB
testcase_04	AC	323 ms; 6,940 KB
testcase_05	AC	57 ms; 6,944 KB
testcase_06	AC	157 ms; 6,940 KB
testcase_07	AC	68 ms; 6,940 KB
testcase_08	AC	73 ms; 6,940 KB
testcase_09	AC	145 ms; 6,940 KB
testcase_10	AC	69 ms; 6,940 KB
testcase_11	AC	2 ms; 6,944 KB
testcase_12	TLE	-
testcase_13	--	-
testcase_14	--	-
testcase_15	--	-
testcase_16	--	-
testcase_17	--	-
testcase_18	--	-
testcase_19	--	-
testcase_20	--	-
testcase_21	--	-
testcase_22	--	-
testcase_23	--	-
testcase_24	--	-
testcase_25	--	-

ソースコード

#[allow(unused_imports)]
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, ( $($t:tt),* )) => { ($(read_value!($next, $t)),*) };
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };
    ($next:expr, usize1) => (read_value!($next, usize) - 1);
    ($next:expr, [ $t:tt ]) => {{
        let len = read_value!($next, usize);
        read_value!($next, [$t; len])
    }};
    ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error"));
}

/// 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, 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_234_567_891;
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;
            }
        }
    }
}

mod arbitrary_mod {
    use crate::mod_int;
    use crate::fft;
    const MOD1: i64 = 1012924417;
    const MOD2: i64 = 1224736769;
    const MOD3: i64 = 1007681537;
    const G1: i64 = 5;
    const G2: i64 = 3;
    const G3: i64 = 3;
    define_mod!(P1, MOD1);
    define_mod!(P2, MOD2);
    define_mod!(P3, MOD3);

    fn zmod(mut a: i64, b: i64) -> i64 {
        a %= b;
        if a < 0 {
            a += b;
        }
        a
    }
    fn ext_gcd(mut a: i64, mut b: i64) -> (i64, i64, i64) {
        let mut x = 0;
        let mut y = 1;
        let mut u = 1;
        let mut v = 0;
        while a != 0 {
            let q = b / a;
            x -= q * u;
            std::mem::swap(&mut x, &mut u);
            y -= q * v;
            std::mem::swap(&mut y, &mut v);
            b -= q * a;
            std::mem::swap(&mut b, &mut a);
        }
        (b, x, y)
    }
    fn invmod(a: i64, b: i64) -> i64 {
        let x = ext_gcd(a, b).1;
        zmod(x, b)
    }

    // This function is ported from http://math314.hateblo.jp/entry/2015/05/07/014908
    fn garner(mut mr: Vec<(i64, i64)>, mo: i64) -> i64 {
        mr.push((mo, 0));

        let mut coffs = vec![1; mr.len()];
        let mut constants = vec![0; mr.len()];
        for i in 0..mr.len() - 1 {
            let v = zmod(mr[i].1 - constants[i], mr[i].0) * invmod(coffs[i], mr[i].0) % mr[i].0;
            assert!(v >= 0);
            for j in i + 1..mr.len() {
                constants[j] += coffs[j] * v % mr[j].0;
                constants[j] %= mr[j].0;
                coffs[j] = coffs[j] * mr[i].0 % mr[j].0;
            }
        }
        constants[mr.len() - 1]
    }

    // f *= g, g is destroyed
    fn convolution_friendly<P: mod_int::Mod>(a: &[i64], b: &[i64], gen: i64) -> Vec<i64> {
        use mod_int::ModInt;
        let d = a.len();
        let mut f = vec![ModInt::<P>::new(0); d];
        let mut g = vec![ModInt::<P>::new(0); d];
        for i in 0..d {
            f[i] = a[i].into();
            g[i] = b[i].into();
        }
        let zeta = ModInt::new(gen).pow((P::m() - 1) / d as i64);
        fft::fft(&mut f, zeta, ModInt::new(1));
        fft::fft(&mut g, zeta, ModInt::new(1));
        for i in 0..d {
            f[i] *= g[i];
        }
        fft::inv_fft(&mut f, zeta.inv(), ModInt::new(1));
        let inv = ModInt::new(d as i64).inv();
        let mut ans = vec![0; d];
        for i in 0..d {
            ans[i] = (f[i] * inv).x;
        }
        ans
    }


    pub fn arbmod_convolution(a: &mut [i64], b: &mut [i64], mo: i64)
                          -> Vec<i64> {
        use mod_int::Mod;
        let d = a.len();
        assert!(d.is_power_of_two());
        assert_eq!(d, b.len());
        for x in a.iter_mut() {
            *x = zmod(*x, mo);
        }
        for x in b.iter_mut() {
            *x = zmod(*x, mo);
        }
        let x = convolution_friendly::<P1>(&a, &b, G1);
        let y = convolution_friendly::<P2>(&a, &b, G2);
        let z = convolution_friendly::<P3>(&a, &b, G3);

        let mut ret = vec![0; d];
        let mut mr = [(0, 0); 3];
        for i in 0..d {
            mr[0] = (P1::m(), x[i]);
            mr[1] = (P2::m(), y[i]);
            mr[2] = (P3::m(), z[i]);
            ret[i] = garner(mr.to_vec(), mo);
        }
        ret
    }
}

// f *= g, g is destroyed
fn convolution(f: &mut [MInt], g: &[MInt]) {
    let mut a = vec![0; f.len()];
    let mut b = vec![0; g.len()];
    for i in 0..f.len() {
        a[i] = f[i].x;
    }
    for i in 0..g.len() {
        b[i] = g[i].x;
    }
    let ans = arbitrary_mod::arbmod_convolution(&mut a, &mut b, MOD);
    for i in 0..f.len() {
        f[i] = ans[i].into();
    }
}

fn bostan_mori(a: &[MInt], b: &[MInt], mut e: i64) -> MInt {
    let n = a.len();
    let mut len = 1;
    while len <= 2 * n {
        len *= 2;
    }
    assert_eq!(b.len(), n + 1);
    let mut a = a.to_vec();
    let mut b = b.to_vec();
    let mut c = vec![MInt::new(0); len];
    let mut d = vec![MInt::new(0); len];
    while e > 0 {
        for i in 0..2 * n + 1 {
            c[i] = 0.into();
        }
        for i in 0..n + 1 {
            d[i] = 0.into();
        }
        let r = (e % 2) as usize;
        for j in 0..n + 1 {
            let coef = if j % 2 == 0 { b[j] } else { -b[j] };
            d[j] = coef;
        }
        for j in 0..n {
            c[j] = a[j];
        }
        convolution(&mut c, &d);
        for i in 0..n {
            a[i] = c[2 * i + r];
        }
        for i in 0..2 * n {
            c[i] = 0.into();
        }
        for j in 0..n + 1 {
            c[j] = b[j];
        }
        convolution(&mut c, &d);
        for i in 0..n + 1 {
            b[i] = c[2 * i];
        }
        e /= 2;
    }
    a[0] * b[0].inv()
}

// Tags: bostan-mori
fn main() {
    // In order to avoid potential stack overflow, spawn a new thread.
    let stack_size = 104_857_600; // 100 MB
    let thd = std::thread::Builder::new().stack_size(stack_size);
    thd.spawn(|| solve()).unwrap().join().unwrap();
}

fn solve() {
    input! {
        n: usize, m: i64,
        a: [usize; n],
    }
    const W: usize = 25_000;
    let mut dp = vec![MInt::new(0); W];
    dp[0] = 1.into();
    let mut sz = 0;
    for a in a {
        for j in (0..W - a).rev() {
            dp[j + a] = dp[j + a] - dp[j];
        }
        sz += a;
    }
    let mut tmp = vec![MInt::new(0); sz];
    tmp[0] = 1.into();
    println!("{}", bostan_mori(&tmp, &dp[..sz + 1], m));
}