use std::io::Write; fn run() { input! { n: usize, q: usize, a: [i64; n], d: [i64; q], } let mut b = a.windows(2).map(|a| a[1] - a[0]).collect::>(); let mut sb = b.clone(); b.sort(); let mut sum = b.clone(); sum.insert(0, 0); sb.insert(0, 0); for i in 1..sum.len() { sum[i] += sum[i - 1]; sb[i] += sb[i - 1]; } let mut cht = IncrementalCHT::new(); for i in 0..sb.len() { let a = -(i as i64) + (n - 1 - i) as i64; let b = sb[i] - (sb[n - 1] - sb[i]); cht.add_line(-a, -b); } let out = std::io::stdout(); let mut out = std::io::BufWriter::new(out.lock()); for d in d { let pos = b.upper_bound(&d); let l = pos as i64 * d - sum[pos]; let r = sum[n - 1] - sum[pos] - (n - 1 - pos) as i64 * d; let need = -cht.find(d); let ans = need + (l + r - need) / 2; writeln!(out, "{}", ans).ok(); } } fn main() { run(); } // ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 #[macro_export] 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_export] 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_export] macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ---------- end input macro ---------- // ---------- begin super slice ---------- pub trait SuperSlice { type Item; fn lower_bound(&self, key: &Self::Item) -> usize where Self::Item: Ord; fn lower_bound_by(&self, f: F) -> usize where F: FnMut(&Self::Item) -> std::cmp::Ordering; fn lower_bound_by_key(&self, key: &K, f: F) -> usize where K: Ord, F: FnMut(&Self::Item) -> K; fn upper_bound(&self, key: &Self::Item) -> usize where Self::Item: Ord; fn upper_bound_by(&self, f: F) -> usize where F: FnMut(&Self::Item) -> std::cmp::Ordering; fn upper_bound_by_key(&self, key: &K, f: F) -> usize where K: Ord, F: FnMut(&Self::Item) -> K; fn next_permutation(&mut self) -> bool where Self::Item: Ord; fn next_permutation_by(&mut self, f: F) -> bool where F: FnMut(&Self::Item, &Self::Item) -> std::cmp::Ordering; fn prev_permutation(&mut self) -> bool where Self::Item: Ord; } impl SuperSlice for [T] { type Item = T; fn lower_bound(&self, key: &Self::Item) -> usize where T: Ord, { self.lower_bound_by(|p| p.cmp(key)) } fn lower_bound_by(&self, mut f: F) -> usize where F: FnMut(&Self::Item) -> std::cmp::Ordering, { self.binary_search_by(|p| f(p).then(std::cmp::Ordering::Greater)) .unwrap_err() } fn lower_bound_by_key(&self, key: &K, mut f: F) -> usize where K: Ord, F: FnMut(&Self::Item) -> K, { self.lower_bound_by(|p| f(p).cmp(key)) } fn upper_bound(&self, key: &Self::Item) -> usize where T: Ord, { self.upper_bound_by(|p| p.cmp(key)) } fn upper_bound_by(&self, mut f: F) -> usize where F: FnMut(&Self::Item) -> std::cmp::Ordering, { self.binary_search_by(|p| f(p).then(std::cmp::Ordering::Less)) .unwrap_err() } fn upper_bound_by_key(&self, key: &K, mut f: F) -> usize where K: Ord, F: FnMut(&Self::Item) -> K, { self.upper_bound_by(|p| f(p).cmp(key)) } fn next_permutation(&mut self) -> bool where T: Ord, { self.next_permutation_by(|a, b| a.cmp(b)) } fn next_permutation_by(&mut self, mut f: F) -> bool where F: FnMut(&Self::Item, &Self::Item) -> std::cmp::Ordering, { use std::cmp::Ordering::*; if let Some(x) = self.windows(2).rposition(|a| f(&a[0], &a[1]) == Less) { let y = self.iter().rposition(|b| f(&self[x], b) == Less).unwrap(); self.swap(x, y); self[(x + 1)..].reverse(); true } else { self.reverse(); false } } fn prev_permutation(&mut self) -> bool where T: Ord, { self.next_permutation_by(|a, b| a.cmp(b).reverse()) } } // ---------- end super slice ---------- // 以下のクエリを処理する // add_line(a, b): 直線 ax + b を追加 // find(x): min (ax + b) を返す。空のとき呼ぶとREになる // 計算量 // 直線追加クエリがN回飛んでくるとする // 直線追加 償却O(log N) // 点質問: O((log N)^2) // ---------- begin incremental convex hull trick (min) ---------- // reference: https://yukicoder.me/wiki/decomposable_searching_problem // verify: https://old.yosupo.jp/submission/35150 #[derive(Clone)] struct ConvexHullTrick { line: Vec<(i64, i64)>, } impl ConvexHullTrick { fn new(mut line: Vec<(i64, i64)>) -> Self { assert!(line.len() > 0); line.sort(); line.dedup_by(|a, b| a.0 == b.0); let mut stack: Vec<(i64, i64)> = vec![]; for (a, b) in line { while stack.len() >= 2 { let len = stack.len(); let (c, d) = stack[len - 1]; let (e, f) = stack[len - 2]; let x = (d - b).div_euclid(a - c); let y = (f - d).div_euclid(c - e); if x >= y { stack.pop(); } else { break; } } stack.push((a, b)); } ConvexHullTrick { line: stack } } fn find(&self, x: i64) -> i64 { let mut l = 0; let mut r = self.line.len() - 1; let line = &self.line; let func = |k: usize| -> i64 { let (a, b) = line[k]; a * x + b }; while r - l >= 3 { let ll = (2 * l + r) / 3; let rr = (l + 2 * r) / 3; if func(ll) <= func(rr) { r = rr; } else { l = ll; } } line[l..=r].iter().map(|p| p.0 * x + p.1).min().unwrap() } } #[derive(Clone, Default)] pub struct IncrementalCHT { size: usize, cht: Vec<(ConvexHullTrick, usize)>, } impl IncrementalCHT { pub fn new() -> Self { IncrementalCHT { size: 0, cht: vec![] } } pub fn add_line(&mut self, a: i64, b: i64) { self.size += 1; let mut line = vec![(a, b)]; let mut p = 0; while self.cht.last().map_or(false, |q| q.1 == p) { p += 1; line.append(&mut self.cht.pop().unwrap().0.line); } let cht = ConvexHullTrick::new(line); self.cht.push((cht, p)); } pub fn find(&self, x: i64) -> i64 { self.cht.iter().map(|p| p.0.find(x)).min().unwrap() } pub fn append(&mut self, other: &mut Self) { if self.size < other.size { std::mem::swap(self, other); } for (mut cht, _) in other.cht.drain(..) { for (a, b) in cht.line.drain(..) { self.add_line(a, b); } } other.size = 0; } } // ---------- end incremental convex hull trick (min) ----------