From 5f5deb7b1a219d2fd4222a4e4a5e7ff76c79661d Mon Sep 17 00:00:00 2001
From: koba-e964 <3303362+koba-e964@users.noreply.github.com>
Date: Sun, 30 Jun 2024 00:28:36 +0900
Subject: [PATCH] Add yukicoder/2792.rs yukicoder/2793.rs

---
 yukicoder/2792.rs | 145 +++++++++++++++++++++++++++++++++++++++++++++
 yukicoder/2793.rs | 146 ++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 291 insertions(+)
 create mode 100644 yukicoder/2792.rs
 create mode 100644 yukicoder/2793.rs

diff --git a/yukicoder/2792.rs b/yukicoder/2792.rs
new file mode 100644
index 00000000..41278bc9
--- /dev/null
+++ b/yukicoder/2792.rs
@@ -0,0 +1,145 @@
+// 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 ; $len:expr ]) => {
+        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
+    };
+    ($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> 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> From<i64> for ModInt<M> {
+        fn from(x: i64) -> Self { Self::new(x) }
+    }
+} // 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 { $modulo } }
+    }
+}
+const MOD: i64 = 998_244_353;
+define_mod!(P, MOD);
+type MInt = mod_int::ModInt<P>;
+
+// Depends on MInt.rs
+fn fact_init(w: usize) -> (Vec<MInt>, Vec<MInt>) {
+    let mut fac = vec![MInt::new(1); w];
+    let mut invfac = vec![0.into(); w];
+    for i in 1..w {
+        fac[i] = fac[i - 1] * i as i64;
+    }
+    invfac[w - 1] = fac[w - 1].inv();
+    for i in (0..w - 1).rev() {
+        invfac[i] = invfac[i + 1] * (i as i64 + 1);
+    }
+    (fac, invfac)
+}
+
+fn main() {
+    input! {
+        n: usize,
+        a: [usize; n],
+    }
+    let (fac, invfac) = fact_init(200_001);
+    let mut tot = MInt::new(0);
+    for i in 0..n {
+        tot += fac[i + a[i] - 1] * invfac[i] * invfac[a[i] - 1];
+        for j in if i + 1 == n { 0 } else { a[i + 1] }..a[i] {
+            tot += fac[i + j] * invfac[i] * invfac[j];
+        }
+    }
+    println!("{}", tot);
+}
diff --git a/yukicoder/2793.rs b/yukicoder/2793.rs
new file mode 100644
index 00000000..36245515
--- /dev/null
+++ b/yukicoder/2793.rs
@@ -0,0 +1,146 @@
+use std::io::{Write, BufWriter};
+// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
+macro_rules! input {
+    ($($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, [ $t:tt ]) => {{
+        let len = read_value!($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> 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> From<i64> for ModInt<M> {
+        fn from(x: i64) -> Self { Self::new(x) }
+    }
+} // 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 { $modulo } }
+    }
+}
+const MOD: i64 = 998_244_353;
+define_mod!(P, MOD);
+type MInt = mod_int::ModInt<P>;
+
+// https://yukicoder.me/problems/no/2793 (4)
+// 実験により、a[i] に掛けるべき重みが f(a[i]; k^{i}) であることがわかる。
+// つまり、i=i のときの遷移の係数に k^{c[0]0 + c[1]1 + ...} を掛けたものの和は f(a[i]; k^{i+1}) である。
+fn main() {
+    let out = std::io::stdout();
+    let mut out = BufWriter::new(out.lock());
+    macro_rules! puts {($($format:tt)*) => (let _ = write!(out,$($format)*););}
+    input! {
+        t: usize,
+        dat: [([i64], i64); t],
+    }
+    for (mut a, rest) in dat {
+        a.push(rest);
+        let k = a[0];
+        let a = a[1..].to_vec();
+        let n = a.len();
+        let mut ans = MInt::new(1);
+        for i in 0..n {
+            let x = MInt::new(k).pow(i as i64 + 1);
+            ans *= x.pow(a[i] - 1) * (x - 1);
+        }
+        puts!("{}\n", ans);
+    }
+}