// 累積xorが一致しないようにしたい // use std::io::Write; use std::collections::*; type Map = BTreeMap; type Set = BTreeSet; type Deque = VecDeque; fn main() { input! { n: usize, k: usize, a: [usize; n], } let mut map = Map::new(); for (i, &a) in a.iter().enumerate() { let mut x = vec![0]; for i in 1..=k { if i < a { x.push(a ^ (a - i)); } x.push(a ^ (a + i)); } x.sort(); x.dedup(); for x in x { map.entry(x).or_insert(vec![]).push(i); } } let mut ban = Map::new(); let mut last = vec![None; 1 << 21]; last[0] = Some(n); let mut xor = 0; let mut r = n; let mut l = 0; for (i, a) in a.iter().enumerate().rev() { xor ^= a; for &x in map.keys() { if let Some(y) = last[xor ^ x] { ban.entry(x).or_insert(vec![]).push((i, y)); } } if let Some(y) = last[xor] { l = l.max(i); r = r.min(y); } last[xor] = Some(i); } if l >= r { println!("No"); return; } for (x, pos) in map { let po = ban.entry(x).or_insert(vec![]); po.sort_by_key(|p| (p.0, !p.1)); po.dedup_by(|a, b| b.1 >= a.0 && { b.1 = b.1.max(a.1); true }); for &pos in pos.iter() { if !(l <= pos && pos < r) { continue; } let u = po.upper_bound_by_key(&pos, |p| p.0); if u == 0 || po[u - 1].1 <= pos { println!("Yes"); return; } } } println!("No"); } // ---------- 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 ----------