This documentation is automatically generated by online-judge-tools/verification-helper
// #define PROBLEM "https://atcoder.jp/contests/abc223/tasks/abc223_h"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/lesson/2/ITP1/1/ITP1_1_A"
/*
* AtCoder Beginner Contest 223 H - Xor Query
* https://atcoder.jp/contests/abc223/submissions/68663949
*/
#include "../../Src/Sequence/OfflineRangeProduct.hpp"
#include <iostream>
#include <array>
#include <bit>
#include <vector>
using namespace zawa;
using namespace std;
struct M {
using Element = array<unsigned long long, 60>;
static unsigned long long reduce(const Element& B, unsigned long long v) {
for (int i = 59 ; i >= 0 and v ; i--)
if (v & (1ull << i))
v ^= B[i];
return v;
}
static bool insert(Element& B, unsigned long long v) {
v = reduce(B, v);
if (v) {
B[bit_width(v) - 1] = v;
return true;
}
return false;
}
static Element identity() {
Element res;
res.fill(0);
return res;
}
static Element operation(Element l, Element r) {
for (unsigned long long v : r)
if (v)
insert(l, v);
return l;
}
static Element acted(Element l, unsigned long long v) {
insert(l, v);
return l;
}
};
struct query {
int l, r;
};
int main() {
#ifdef ATCODER
cin.tie(0);
cout.tie(0);
ios::sync_with_stdio(0);
int N, Q;
cin >> N >> Q;
vector<unsigned long long> A(N), X(Q);
for (int i = 0 ; i < N ; i++)
cin >> A[i];
vector<query> lr(Q);
for (int i = 0 ; i < Q ; i++) {
int l, r;
cin >> l >> r >> X[i];
l--;
lr[i] = {l, r};
}
auto ans = OfflineRangeProduct<M>(A, lr);
for (int i = 0 ; i < Q ; i++)
cout << (M::reduce(ans[i], X[i]) == 0 ? "Yes\n" : "No\n");
#else
cout << "Hello World\n";
#endif
}
#line 1 "Test/AtCoder/abc223_h.test.cpp"
// #define PROBLEM "https://atcoder.jp/contests/abc223/tasks/abc223_h"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/lesson/2/ITP1/1/ITP1_1_A"
/*
* AtCoder Beginner Contest 223 H - Xor Query
* https://atcoder.jp/contests/abc223/submissions/68663949
*/
#line 2 "Src/Sequence/OfflineRangeProduct.hpp"
#line 2 "Src/Template/TypeAlias.hpp"
#include <cstdint>
#include <cstddef>
namespace zawa {
using i16 = std::int16_t;
using i32 = std::int32_t;
using i64 = std::int64_t;
using i128 = __int128_t;
using u8 = std::uint8_t;
using u16 = std::uint16_t;
using u32 = std::uint32_t;
using u64 = std::uint64_t;
using usize = std::size_t;
} // namespace zawa
#line 2 "Src/Algebra/Monoid/MonoidConcept.hpp"
#line 2 "Src/Algebra/Semigroup/SemigroupConcept.hpp"
#include <concepts>
namespace zawa {
namespace concepts {
template <class T>
concept Semigroup = requires {
typename T::Element;
{ T::operation(std::declval<typename T::Element>(), std::declval<typename T::Element>()) } -> std::same_as<typename T::Element>;
};
} // namespace concepts
} // namespace zawa
#line 4 "Src/Algebra/Monoid/MonoidConcept.hpp"
#line 6 "Src/Algebra/Monoid/MonoidConcept.hpp"
namespace zawa {
namespace concepts {
template <class T>
concept Identitiable = requires {
typename T::Element;
{ T::identity() } -> std::same_as<typename T::Element>;
};
template <class T>
concept Monoid = Semigroup<T> and Identitiable<T>;
} // namespace
} // namespace zawa
#line 2 "Src/Algebra/Action/ActionConcept.hpp"
#line 4 "Src/Algebra/Action/ActionConcept.hpp"
namespace zawa {
namespace concepts {
template <class G, class X>
concept Action = requires {
typename G::Element;
{ G::action(std::declval<typename G::Element>(), std::declval<X>()) } -> std::same_as<X>;
};
// Is appropriate name X-set?
template <class G, class X>
concept Acted = requires {
typename G::Element;
{ G::acted(std::declval<typename G::Element>(), std::declval<X>()) } -> std::same_as<typename G::Element>;
};
} // namespace concepts
} // namespace zawa
#line 6 "Src/Sequence/OfflineRangeProduct.hpp"
#include <algorithm>
#include <cassert>
#line 10 "Src/Sequence/OfflineRangeProduct.hpp"
#include <numeric>
#include <vector>
namespace zawa {
namespace offline_range_product_internal {
template <class R>
concept Range = requires (R lr) {
{ lr.l } -> std::convertible_to<usize>;
{ lr.r } -> std::convertible_to<usize>;
};
template <class M, class S, class R>
concept condition = concepts::Monoid<M> and Range<R> and (std::same_as<typename M::Element, S> or concepts::Acted<M, S>);
} // namespace offline_range_product_internal
template <class M, class S, class Range>
requires offline_range_product_internal::condition<M, S, Range>
std::vector<typename M::Element> OfflineRangeProduct(const std::vector<S>& as, const std::vector<Range>& qs) {
std::vector<typename M::Element> sum(as.size() + 1), res(qs.size(), M::identity());
auto f = [&](usize m, const std::vector<usize>& idx) -> void {
sum[m] = M::identity();
usize L = m, R = m;
for (usize i : idx) {
L = std::min<usize>(L, qs[i].l);
R = std::max<usize>(R, qs[i].r);
}
for (usize i = m ; i-- > L ; ) {
if constexpr (std::same_as<typename M::Element, S>)
sum[i] = M::operation(as[i], sum[i + 1]);
else
sum[i] = M::acted(sum[i + 1], as[i]);
}
for (usize i = m ; i < R ; i++) {
if constexpr (std::same_as<typename M::Element, S>)
sum[i + 1] = M::operation(sum[i], as[i]);
else
sum[i + 1] = M::acted(sum[i], as[i]);
}
for (usize i : idx)
res[i] = M::operation(sum[qs[i].l], sum[qs[i].r]);
};
auto rec = [&](auto rec, usize L, usize R, std::vector<usize> idx) -> void {
if (L >= R)
return;
if (L + 1 == R) {
f(L, idx);
return;
}
const usize mid = (L + R) / 2;
std::vector<usize> toL, toR, cur;
for (auto&& i : idx) {
assert(qs[i].l <= qs[i].r and static_cast<usize>(qs[i].r) <= as.size());
if (static_cast<usize>(qs[i].r) <= mid)
toL.push_back(std::move(i));
else if (mid <= static_cast<usize>(qs[i].l))
toR.push_back(std::move(i));
else
cur.push_back(std::move(i));
}
if (cur.size())
f(mid, cur);
if (toL.size())
rec(rec, L, mid, toL);
if (toR.size())
rec(rec, mid, R, toR);
};
std::vector<usize> idx(qs.size());
std::iota(idx.begin(), idx.end(), 0);
rec(rec, 0, as.size(), idx);
return res;
}
} // namespace zawa
#line 10 "Test/AtCoder/abc223_h.test.cpp"
#include <iostream>
#include <array>
#include <bit>
#line 15 "Test/AtCoder/abc223_h.test.cpp"
using namespace zawa;
using namespace std;
struct M {
using Element = array<unsigned long long, 60>;
static unsigned long long reduce(const Element& B, unsigned long long v) {
for (int i = 59 ; i >= 0 and v ; i--)
if (v & (1ull << i))
v ^= B[i];
return v;
}
static bool insert(Element& B, unsigned long long v) {
v = reduce(B, v);
if (v) {
B[bit_width(v) - 1] = v;
return true;
}
return false;
}
static Element identity() {
Element res;
res.fill(0);
return res;
}
static Element operation(Element l, Element r) {
for (unsigned long long v : r)
if (v)
insert(l, v);
return l;
}
static Element acted(Element l, unsigned long long v) {
insert(l, v);
return l;
}
};
struct query {
int l, r;
};
int main() {
#ifdef ATCODER
cin.tie(0);
cout.tie(0);
ios::sync_with_stdio(0);
int N, Q;
cin >> N >> Q;
vector<unsigned long long> A(N), X(Q);
for (int i = 0 ; i < N ; i++)
cin >> A[i];
vector<query> lr(Q);
for (int i = 0 ; i < Q ; i++) {
int l, r;
cin >> l >> r >> X[i];
l--;
lr[i] = {l, r};
}
auto ans = OfflineRangeProduct<M>(A, lr);
for (int i = 0 ; i < Q ; i++)
cout << (M::reduce(ans[i], X[i]) == 0 ? "Yes\n" : "No\n");
#else
cout << "Hello World\n";
#endif
}