fn main() { input! { n: usize, m: usize, k: i64, b: [i64; n], r: [i64; m], } let mut b = b.into_iter().map(|b| (b % k, b / k)).collect::>(); let mut r = r.into_iter().map(|r| (r % k, r / k)).collect::>(); b.sort(); r.sort(); let mut sum = 0; let mut cnt = 0; let mut x = 0; let mut y = 0; while x < b.len() && y < r.len() { let v = b[x].0.min(r[y].0); let b = b[x..].iter().take_while(|b| b.0 == v).map(|b| b.1).collect::>(); let r = r[y..].iter().take_while(|b| b.0 == v).map(|b| b.1).collect::>(); x += b.len(); y += r.len(); let dp = matching1d(b, r); sum += *dp.last().unwrap(); cnt += dp.len() - 1; } if cnt == n.min(m) { println!("{}", sum); } else { println!("-1"); } } // A_i と B_j をマッチさせるときに |A_i - B_j| のコスト // k 個(0 <= k <= min(|A|, |B|)) マッチングを作るときの最小コスト fn matching1d(a: Vec, b: Vec) -> Vec { let m = b.len(); let mut z = vec![]; z.extend(a.into_iter().map(|a| (a, 0))); z.extend(b.into_iter().map(|a| (a, 1))); z.sort(); let mut sum = vec![0; z.len() + 1]; let mut last = vec![z.len() + 1; z.len() + 1]; let mut pos = m; last[pos] = z.len(); for (i, &(x, op)) in z.iter().enumerate().rev() { if op == 1 { pos -= 1; } else { pos += 1; } let r = last[pos]; if r < sum.len() { sum[i] = (z[r - 1].0 - x).abs() + sum[i + 1] - sum[r - 1] + sum[r]; } last[pos] = i; } let mut set = FastSet::build(z.len(), 0..z.len()); let mut h = std::collections::BinaryHeap::new(); for (i, z) in z.windows(2).enumerate() { if z[0].1 != z[1].1 { let d = sum[i] - sum[i + 2]; h.push((-d, i, i + 1)); } } let mut ans = vec![0]; while let Some((d, l, r)) = h.pop() { if !set.contains(l) || !set.contains(r) { continue; } let v = *ans.last().unwrap() - d; ans.push(v); set.remove(l); set.remove(r); let nl = set.prev(l); let nr = set.next(r); let nlr = nl.zip(nr); if nlr.map_or(false, |(s, t)| z[s].1 != z[t].1) { let (s, t) = nlr.unwrap(); let d = sum[s] - sum[t + 1] - (sum[s + 1] - sum[t]); h.push((-d, s, t)); } } ans } // ---------- 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 ---------- pub struct FastSet { size: usize, seg: Vec>, } impl FastSet { pub fn build(size: usize, init: I) -> Self where I: Iterator { assert!(size > 0); let mut n = size; let w = std::mem::size_of::() * 8; let mut seg = vec![]; let mut data = vec![0; (n + w - 1) / w]; for x in init { assert!(x < size); data[x / w] |= 1 << (x % w); } seg.push(data); while n > 1 { n = (n + w - 1) / w; let d = seg.last().unwrap().chunks(w).map(|a| { a.iter().enumerate().filter(|p| *p.1 > 0).fold(0, |s, a| s | (1 << a.0)) }).collect::>(); seg.push(d); } Self { size, seg } } pub fn new(size: usize) -> Self { let mut n = size; let w = std::mem::size_of::() * 8; let mut seg = vec![]; while { let m = (n + w - 1) / w; seg.push(vec![0; m]); n = m; n > 1 } {} Self { size, seg } } pub fn insert(&mut self, mut x: usize) -> bool { assert!(x < self.size); let w = std::mem::size_of::() * 8; let seg = &mut self.seg; if seg[0][x / w] >> (x % w) == 1 { return false; } for seg in seg.iter_mut() { seg[x / w] |= 1 << (x % w); x /= w; } true } pub fn remove(&mut self, mut x: usize) -> bool { assert!(x < self.size); let w = std::mem::size_of::() * 8; let seg = &mut self.seg; if seg[0][x / w] >> (x % w) == 0 { return false; } for seg in seg.iter_mut() { seg[x / w] &= !(1 << (x % w)); if seg[x / w] != 0 { break; } x /= w; } true } pub fn contains(&self, x: usize) -> bool { assert!(x < self.size); let w = std::mem::size_of::() * 8; self.seg[0][x / w] >> (x % w) & 1 == 1 } pub fn next(&self, mut x: usize) -> Option { if x >= self.size { return None; } let w = std::mem::size_of::() * 8; let seg = &self.seg; for (i, s) in seg.iter().enumerate() { if x / w == s.len() { return None; } if s[x / w] >> (x % w) == 0 { x = x / w + 1; continue; } let k = (s[x / w] >> (x % w)).trailing_zeros() as usize; x += k; for seg in seg[..i].iter().rev() { let k = seg[x].trailing_zeros() as usize; x = w * x + k; } return Some(x) } None } pub fn prev(&self, mut x: usize) -> Option { x = x.min(self.size - 1); let w = std::mem::size_of::() * 8; let seg = &self.seg; for (i, s) in seg.iter().enumerate() { let d = s[x / w] << (w - 1 - x % w); if d == 0 { if x < w { break; } x = x / w - 1; continue; } let k = d.leading_zeros() as usize; x -= k; for seg in seg[..i].iter().rev() { let k = w - 1 - seg[x].leading_zeros() as usize; x = w * x + k; } return Some(x); } None } }