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 ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } /** * Segment Tree. This data structure is useful for fast folding on intervals of an array * whose elements are elements of monoid I. Note that constructing this tree requires the identity * element of I and the operation of I. * Verified by: yukicoder No. 259 (http://yukicoder.me/submissions/100581) * AGC015-E (http://agc015.contest.atcoder.jp/submissions/1461001) */ struct SegTree { n: usize, dat: Vec, op: BiOp, e: I, } impl SegTree where BiOp: Fn(I, I) -> I, I: Copy { pub fn new(n_: usize, op: BiOp, e: I) -> Self { let mut n = 1; while n < n_ { n *= 2; } // n is a power of 2 SegTree {n: n, dat: vec![e; 2 * n - 1], op: op, e: e} } /* ary[k] <- v */ pub fn update(&mut self, idx: usize, v: I) { let mut k = idx + self.n - 1; self.dat[k] = v; while k > 0 { k = (k - 1) / 2; self.dat[k] = (self.op)(self.dat[2 * k + 1], self.dat[2 * k + 2]); } } /* [a, b) (note: half-inclusive) * http://proc-cpuinfo.fixstars.com/2017/07/optimize-segment-tree/ */ pub fn query(&self, mut a: usize, mut b: usize) -> I { let mut left = self.e; let mut right = self.e; a += self.n - 1; b += self.n - 1; while a < b { if (a & 1) == 0 { left = (self.op)(left, self.dat[a]); } if (b & 1) == 0 { right = (self.op)(self.dat[b - 1], right); } a = a / 2; b = (b - 1) / 2; } (self.op)(left, right) } // Find x in [a, b] s.t. f(range([x, b))) and x is minimum possible, // or b + 1 if there is no such x. pub fn binary_search_left bool>( &self, a: usize, b: usize, f: F, ) -> usize { if !f(self.e) { return b + 1; } if b == 0 { return 0; } let x = self.min_left(b + self.n - 1, &f); std::cmp::max(a, x) } // Port from https://github.com/atcoder/ac-library/blob/master/atcoder/segtree.hpp fn min_left bool>( &self, mut r: usize, f: &F, ) -> usize { let mut sm = self.e; loop { r -= 1; while r > 0 && r % 2 == 0 { r = (r - 1) / 2; } if !f((self.op)(self.dat[r], sm)) { while r < self.n - 1 { r = 2 * r + 2; let val = (self.op)(self.dat[r], sm); if f(val) { sm = val; r -= 1; } } return r + 2 - self.n; } sm = (self.op)(self.dat[r], sm); if (r + 1).is_power_of_two() { break; } } return 0; } } // Tags: binary-search-on-segtrees, greedy-algorithm 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, a: [i64; n], q: usize, b: [i64; q], } let mut st = SegTree::new(n, |x, y| x | y, 0i64); for i in 0..n { st.update(i, a[i]); } let whole = (1i64 << 60) - 1; for b in b { let mut targ = b; let mut rem = whole; let mut cur = n; let mut ok = true; let mut ans = 0; let last = a[n - 1]; if (last & b) != last { targ ^= rem; ans += 1; if (targ & last) != last { ok = false; } } while cur > 1 && rem != 0 && ok { assert_eq!(rem & targ, targ); let pass = st.binary_search_left(1, cur, |o| ((o & rem) | targ) == targ); if pass == cur { ok = false; break; } let o = st.query(pass, cur); // eprintln!("b = {}, [{}, {}) o = {} ({} <= {})", b, pass - 1, cur, o, targ, rem); rem &= !o; targ &= rem; cur = pass; if cur != 1 { targ ^= rem; ans += 1; } } let fst = a[0]; ok &= targ == (fst & rem) || targ == (!fst & rem); if targ != (fst & rem) { ans += 1; } puts!("{}\n", if ok { ans } else { -1 }); } }