#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; 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, chars) => { read_value!($next, String).chars().collect::>() }; ($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 { 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

; // Sparse Table. // BiOp should be the type of a binary operator which is // associative, commutative and idempotent. // (For example, both min and gcd satisfy these properties.) // Verified by: yukicoder No. 2171 // (https://yukicoder.me/submissions/883410) struct SparseTable { biop: BiOp, st: Vec>, } impl SparseTable where BiOp: Fn(T, T) -> T, T: Copy { pub fn new(ary: &[T], biop: BiOp) -> Self { let n = ary.len(); let mut h = 1; while 1 << h < n { h += 1; } let mut st: Vec> = vec![Vec::from(ary); h + 1]; for i in 0 .. n { st[0][i] = ary[i]; } for b in 1 .. (h + 1) { if n + 1 < 1 << b { break; } for i in 0 .. (n + 1 - (1 << b)) { let next_idx = (1 << (b - 1)) + i; st[b][i] = biop(st[b - 1][i], st[b - 1][next_idx]); } } SparseTable {biop: biop, st: st} } fn top_bit(t: usize) -> usize { 8 * std::mem::size_of::() - 1 - t.leading_zeros() as usize } pub fn query(&self, range: std::ops::Range) -> T { let (f, s) = (range.start, range.end - 1); assert!(f <= s); let b = Self::top_bit(s + 1 - f); let endpoint = s + 1 - (1 << b); (self.biop)(self.st[b][f], self.st[b][endpoint]) } } 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, a: [i64; n], lr: [(usize1, usize); q], } let mut pw = vec![MInt::new(0); n + 1]; pw[0] += 1; for i in 1..n + 1 { pw[i] = pw[i - 1] * 2; } let mut acc = vec![MInt::new(0); n + 1]; for i in (0..n).rev() { acc[i] = acc[i + 1] * 2 + a[i]; } let mut st = vec![]; let mut elim = vec![0; n]; for i in (0..n).rev() { while let Some((val, idx)) = st.pop() { if val <= a[i] { elim[idx] = i + 1; continue; } else { st.push((val, idx)); break; } } st.push((a[i], i)); } for (_, idx) in st { elim[idx] = 0; } let spt = SparseTable::new(&elim, max); // eprintln!("elim = {:?}", elim); for (l, r) in lr { let idx = max(l, spt.query(l..r)); puts!("{}\n", acc[idx + 1] - acc[r] * pw[r - idx - 1] + a[idx]); } }