結果

問題 No.1261 数字集め
ユーザー akakimidori
提出日時 2020-10-16 23:43:28
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 3,045 ms / 8,000 ms
コード長 13,226 bytes
コンパイル時間 12,405 ms
コンパイル使用メモリ 379,988 KB
実行使用メモリ 191,472 KB
最終ジャッジ日時 2024-07-21 04:57:02
合計ジャッジ時間 133,817 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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ファイルパターン 結果
other AC * 94
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ソースコード

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プレゼンテーションモードにする

// ---------- 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 Matrix ----------
#[allow(dead_code)]
mod matrix {
    use std::ops::{Add, Mul};
    pub trait SemiRing: Add<Output = Self> + Mul<Output = Self> + Copy {
        fn zero() -> Self;
        fn one() -> Self;
    }
    pub const SIZE: usize = 3;
    #[derive(Clone)]
    pub struct SquareMatrix<T: SemiRing> {
        buf: [[T; SIZE]; SIZE],
    }
    impl<T: SemiRing> SquareMatrix<T> {
        pub fn zero() -> Self {
            let z = T::zero();
            SquareMatrix {
                buf: [[z; SIZE]; SIZE],
            }
        }
        pub fn identity() -> Self {
            let mut m = Self::zero();
            for i in 0..SIZE {
                m.buf[i][i] = T::one();
            }
            m
        }
        pub fn set_at(&mut self, i: usize, j: usize, v: T) {
            self.buf[i][j] = v;
        }
        pub fn get_at(&self, i: usize, j: usize) -> T {
            self.buf[i][j]
        }
        pub fn matmul(&self, rhs: &Self) -> Self {
            let mut res = Self::zero();
            for (x, a) in res.buf.iter_mut().zip(self.buf.iter()) {
                for (a, b) in a.iter().zip(rhs.buf.iter()) {
                    for (x, b) in x.iter_mut().zip(b.iter()) {
                        *x = *x + *a * *b;
                    }
                }
            }
            res
        }
        pub fn matadd(&self, rhs: &Self) -> Self {
            let mut c = Self::zero();
            for (c, (a, b)) in c.buf.iter_mut().zip(self.buf.iter().zip(rhs.buf.iter())) {
                for (c, (a, b)) in c.iter_mut().zip(a.iter().zip(b.iter())) {
                    *c = *a + *b;
                }
            }
            c
        }
        pub fn matpow(&self, mut n: usize) -> Self {
            let mut t = Self::identity();
            let mut s = self.clone();
            while n > 0 {
                if n & 1 == 1 {
                    t = t.matmul(&s);
                }
                s = s.matmul(&s);
                n >>= 1;
            }
            t
        }
    }
}
// ---------- end Matrix ----------
// ---------- 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 ----------
// クエリなしの時どうやって解くの
// パス1 -> a -> b -> N を全列挙できるとして
// sum (x + y + z == m - 3) (A_a - 1) ^ x * (A_b - 1) ^ y * (A_n - 1) ^ z
// これらの和
// これ求められん...
// 行列累乗でなんとかごまかせるが許されるか？
//
// クエリ
// X -> Yを追加するとできるパスってなんだ？
// Y = N なら
// 1 -> z -> X -> Y
// Y != N なら
// 1 -> X -> Y -> N
// のどれか
// その度に列挙、足しこむのって大丈夫か？
//
use std::io::Write;
use matrix::*;
use modint::*;
type M = ModInt<Mod>;
type Mat = SquareMatrix<M>;
impl SemiRing for M {
    fn zero() -> Self {
        M::zero()
    }
    fn one() -> Self {
        M::one()
    }
}
fn run() {
    input! {
        n: usize,
        m: usize,
        a: [usize; n - 1],
        q: usize,
        ask: [(usize, usize); q],
    }
    let mut a = a;
    a.insert(0, 1);
    a.insert(0, 1);
    let a = a.into_iter().map(|a| M::from(a - 1)).collect::<Vec<_>>();
    let mut ans = M::zero();
    let mut from = vec![vec![]; n + 1];
    let mut to = vec![false; n + 1];
    for i in 2..n {
        to[i] = n % i == 0;
        let mut j = 2 * i;
        while j < n {
            if n % j == 0 {
                let mut mat = Mat::zero();
                mat.set_at(0, 0, a[i]);
                mat.set_at(1, 0, a[j]);
                mat.set_at(1, 1, a[j]);
                mat.set_at(2, 0, a[n]);
                mat.set_at(2, 1, a[n]);
                mat.set_at(2, 2, a[n]);
                let pow = mat.matpow(m - 3);
                for i in 0..3 {
                    ans += pow.get_at(i, 0);
                }
            } else {
                from[j].push(i);
            }
            j += i;
        }
    }
    let out = std::io::stdout();
    let mut out = std::io::BufWriter::new(out.lock());
    writeln!(out, "{}", ans).ok();
    for (x, y) in ask {
        if y == n {
            for &z in from[x].iter() {
                let mut mat = Mat::zero();
                mat.set_at(0, 0, a[z]);
                mat.set_at(1, 0, a[x]);
                mat.set_at(1, 1, a[x]);
                mat.set_at(2, 0, a[y]);
                mat.set_at(2, 1, a[y]);
                mat.set_at(2, 2, a[y]);
                let pow = mat.matpow(m - 3);
                for i in 0..3 {
                    ans += pow.get_at(i, 0);
                }
            }
            to[x] = true;
        } else {
            if to[y] {
                let mut mat = Mat::zero();
                mat.set_at(0, 0, a[x]);
                mat.set_at(1, 0, a[y]);
                mat.set_at(1, 1, a[y]);
                mat.set_at(2, 0, a[n]);
                mat.set_at(2, 1, a[n]);
                mat.set_at(2, 2, a[n]);
                let pow = mat.matpow(m - 3);
                for i in 0..3 {
                    ans += pow.get_at(i, 0);
                }
            }
            from[y].push(x);
        }
        writeln!(out, "{}", ans).ok();
    }
}
fn main() {
    run();
}
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