use std::cmp::*; 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, $t)).collect::>() }; ($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 { pub x: i64, phantom: ::std::marker::PhantomData } impl ModInt { // 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 Default for ModInt { fn default() -> Self { Self::new_internal(0) } } impl>> Add for ModInt { 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>> Sub for ModInt { 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>> Mul for ModInt { type Output = Self; fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) } } impl>> AddAssign for ModInt { fn add_assign(&mut self, other: T) { *self = *self + other; } } impl>> SubAssign for ModInt { fn sub_assign(&mut self, other: T) { *self = *self - other; } } impl>> MulAssign for ModInt { fn mul_assign(&mut self, other: T) { *self = *self * other; } } impl Neg for ModInt { type Output = Self; fn neg(self) -> Self { ModInt::new(0) - self } } impl ::std::fmt::Display for ModInt { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result { self.x.fmt(f) } } impl ::std::fmt::Debug for ModInt { 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 From for ModInt { 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 = 998_244_353; define_mod!(P, MOD); type MInt = mod_int::ModInt

; // comp(f, g) = g o f fn comp((a, b): (MInt, MInt), (c, d): (MInt, MInt)) -> (MInt, MInt) { (a * c, b * c + d) } // https://yukicoder.me/problems/no/1891 (4) // a_i != 0 なのでそれぞれの線形変換には逆変換が存在する。 // s = floor(log_2 N / 2) として 0 <= k < 2^s なる i に対して f_{i xor k} の累積積およびその逆元を保持しておくと、それぞれのクエリは 2^{log_2 N - s} = O(sqrt(N))-time でできる。 // 時間は O((N+Q)sqrt(N))、空間は O(N + Q) 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! { n: usize, q: usize, ab: [(i64, i64); n], lrpx: [(usize, usize, usize, i64); q], } let mut f = vec![(MInt::new(0), MInt::new(0)); n]; let mut invf = vec![(MInt::new(0), MInt::new(0)); n]; for i in 0..n { let (a, b) = ab[i]; let inva = MInt::new(a).inv(); f[i] = (a.into(), b.into()); invf[i] = (inva, -inva * b); } let lgn = (n - 1).count_ones() as usize; let s = (lgn + 1) / 2; let mut qs = vec![vec![]; 1 << s]; for i in 0..q { let (l, r, p, x) = lrpx[i]; let idx = p & ((1 << s) - 1); qs[idx].push((l, r, p & !0usize << s, x, i)); } let mut ans = vec![MInt::new(0); q]; for idx in 0..1 << s { if qs[idx].is_empty() { continue; } let mut acc = vec![(MInt::new(0), MInt::new(0)); n + 1]; let mut invacc = vec![(MInt::new(0), MInt::new(0)); n + 1]; acc[0] = (1.into(), 0.into()); invacc[0] = (1.into(), 0.into()); for i in 0..n { acc[i + 1] = comp(acc[i], f[i ^ idx]); invacc[i + 1] = comp(invf[i ^ idx], invacc[i]); } for &(l, r, p, x, i) in &qs[idx] { let mut prod = MInt::new(x); for b in 0..n >> s { let lo = max(b << s, l); let hi = min((b + 1) << s, r); if lo < hi { let base = b << s ^ p; let (u, v) = invacc[base + lo - (b << s)]; prod = u * prod + v; let (u, v) = acc[base + hi - (b << s)]; prod = u * prod + v; } } ans[i] = prod; } } for a in ans { puts!("{}\n", a); } }