library

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:heavy_check_mark: test_atcoder/abc274_h.test.cpp

Depends on

Code

#define PROBLEM "https://atcoder.jp/contests/abc274/tasks/abc274_Ex"
#include "my_template.hpp"
#include "other/io.hpp"

#include "random/base.hpp"
#include "nt/GF2.hpp"
#include "string/rollinghash_field.hpp"

void solve() {
  LL(N, Q);
  VEC(ll, A, N);
  using F = GF2<60>;
  RollingHash_Field<F> X;
  auto HA = X.build(A);

  FOR(Q) {
    LL(a, b, c, d, e, f);
    --a, --c, --e;
    ll n1 = b - a, n2 = f - e;

    auto check = [&](int n) -> bool {
      // lcp >= n
      if (n1 < n || n2 < n) return false;
      F x1 = X.query(HA, a, a + n);
      F x2 = X.query(HA, c, c + n);
      F x3 = X.query(HA, e, e + n);
      return (x1 + x2) == x3;
    };

    ll n = binary_search(check, 0, N + 1);
    if (n < min(n1, n2)) {
      u64 x = A[a + n] ^ A[c + n];
      u64 y = A[e + n];
      Yes(x < y);
    } else {
      // prefix
      Yes(n1 < n2);
    }
  }
}

signed main() {
  cout << fixed << setprecision(15);

  ll T = 1;
  // LL(T);
  FOR(T) solve();

  return 0;
}
#line 1 "test_atcoder/abc274_h.test.cpp"
#define PROBLEM "https://atcoder.jp/contests/abc274/tasks/abc274_Ex"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない?
// #pragma GCC target("avx2,popcnt")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) \
  for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sm = 0;
  for (auto &&a: A) sm += a;
  return sm;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
  sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}
#endif
#line 1 "other/io.hpp"
#define FASTIO
#include <unistd.h>


// https://judge.yosupo.jp/submission/21623

namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf

uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
  char num[10000][4];
  constexpr Pre() : num() {
    for (int i = 0; i < 10000; i++) {
      int n = i;
      for (int j = 3; j >= 0; j--) {
        num[i][j] = n % 10 | '0';
        n /= 10;
      }
    }
  }
} constexpr pre;

inline void load() {
  memcpy(ibuf, ibuf + pil, pir - pil);
  pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
  pil = 0;
  if (pir < SZ) ibuf[pir++] = '\n';
}

inline void flush() {
  fwrite(obuf, 1, por, stdout);
  por = 0;
}

void rd(char &c) {
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
}

void rd(string &x) {
  x.clear();
  char c;
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
  do {
    x += c;
    if (pil == pir) load();
    c = ibuf[pil++];
  } while (!isspace(c));
}

template <typename T>
void rd_real(T &x) {
  string s;
  rd(s);
  x = stod(s);
}

template <typename T>
void rd_integer(T &x) {
  if (pil + 100 > pir) load();
  char c;
  do
    c = ibuf[pil++];
  while (c < '-');
  bool minus = 0;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (c == '-') { minus = 1, c = ibuf[pil++]; }
  }
  x = 0;
  while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (minus) x = -x;
  }
}

void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }

template <class T, class U>
void rd(pair<T, U> &p) {
  return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
  if constexpr (N < std::tuple_size<T>::value) {
    auto &x = std::get<N>(t);
    rd(x);
    rd_tuple<N + 1>(t);
  }
}
template <class... T>
void rd(tuple<T...> &tpl) {
  rd_tuple(tpl);
}

template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
  for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
  for (auto &d: x) rd(d);
}

void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
  rd(h), read(t...);
}

void wt(const char c) {
  if (por == SZ) flush();
  obuf[por++] = c;
}
void wt(const string s) {
  for (char c: s) wt(c);
}
void wt(const char *s) {
  size_t len = strlen(s);
  for (size_t i = 0; i < len; i++) wt(s[i]);
}

template <typename T>
void wt_integer(T x) {
  if (por > SZ - 100) flush();
  if (x < 0) { obuf[por++] = '-', x = -x; }
  int outi;
  for (outi = 96; x >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[x % 10000], 4);
    x /= 10000;
  }
  if (x >= 1000) {
    memcpy(obuf + por, pre.num[x], 4);
    por += 4;
  } else if (x >= 100) {
    memcpy(obuf + por, pre.num[x] + 1, 3);
    por += 3;
  } else if (x >= 10) {
    int q = (x * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (x - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = x | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}

template <typename T>
void wt_real(T x) {
  ostringstream oss;
  oss << fixed << setprecision(15) << double(x);
  string s = oss.str();
  wt(s);
}

void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }

template <class T, class U>
void wt(const pair<T, U> val) {
  wt(val.first);
  wt(' ');
  wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
  if constexpr (N < std::tuple_size<T>::value) {
    if constexpr (N > 0) { wt(' '); }
    const auto x = std::get<N>(t);
    wt(x);
    wt_tuple<N + 1>(t);
  }
}
template <class... T>
void wt(tuple<T...> tpl) {
  wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
template <class T>
void wt(const vector<T> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}

void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  wt(head);
  if (sizeof...(Tail)) wt(' ');
  print(forward<Tail>(tail)...);
}

// gcc expansion. called automaticall after main.

void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio

using fastio::read;
using fastio::print;
using fastio::flush;

#if defined(LOCAL)
#define SHOW(...) \
  SHOW_IMPL(__VA_ARGS__, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) \
  print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#else
#define SHOW(...)
#endif

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define U32(...)   \
  u32 __VA_ARGS__; \
  read(__VA_ARGS__)
#define U64(...)   \
  u64 __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 4 "test_atcoder/abc274_h.test.cpp"

#line 2 "random/base.hpp"

u64 RNG_64() {
  static uint64_t x_
      = uint64_t(chrono::duration_cast<chrono::nanoseconds>(
                     chrono::high_resolution_clock::now().time_since_epoch())
                     .count())
        * 10150724397891781847ULL;
  x_ ^= x_ << 7;
  return x_ ^= x_ >> 9;
}

u64 RNG(u64 lim) { return RNG_64() % lim; }

ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
#line 1 "nt/GF2.hpp"
#include <emmintrin.h>
#include <smmintrin.h>
#include <wmmintrin.h>

__attribute__((target("pclmul"))) inline __m128i myclmul(const __m128i &a,
                                                         const __m128i &b) {
  return _mm_clmulepi64_si128(a, b, 0);
}

// 2^n 元体
template <int K>
struct GF2 {
  // https://oeis.org/A344141
  // irreducible poly x^K + ...
  static constexpr int POLY[65]
      = {0,  0, 3,  3,   3,  5,   3,  3,  27,  3,  9,  5,   9, 27, 33, 3,   43,
         9,  9, 39, 9,   5,  3,   33, 27, 9,   27, 39, 3,   5, 3,  9,  141, 75,
         27, 5, 53, 63,  99, 17,  57, 9,  39,  89, 33, 27,  3, 33, 45, 113, 29,
         75, 9, 71, 125, 71, 149, 17, 99, 123, 3,  39, 105, 3, 27};

  static constexpr u64 mask() { return u64(-1) >> (64 - K); }

  __attribute__((target("sse4.2"))) static u64 mul(u64 a, u64 b) {
    static bool prepared = 0;
    static u64 MEMO[8][65536];
    if (!prepared) {
      prepared = 1;
      vc<u64> tmp(128);
      tmp[0] = 1;
      FOR(i, 127) {
        tmp[i + 1] = tmp[i] << 1;
        if (tmp[i] >> (K - 1) & 1) {
          tmp[i + 1] ^= POLY[K];
          tmp[i + 1] &= mask();
        }
      }
      FOR(k, 8) {
        MEMO[k][0] = 0;
        FOR(i, 16) {
          FOR(s, 1 << i) { MEMO[k][s | 1 << i] = MEMO[k][s] ^ tmp[16 * k + i]; }
        }
      }
    }
    const __m128i a_ = _mm_set_epi64x(0, a);
    const __m128i b_ = _mm_set_epi64x(0, b);
    const __m128i c_ = myclmul(a_, b_);
    u64 lo = _mm_extract_epi64(c_, 0);
    u64 hi = _mm_extract_epi64(c_, 1);
    u64 x = 0;
    x ^= MEMO[0][lo & 65535];
    x ^= MEMO[1][(lo >> 16) & 65535];
    x ^= MEMO[2][(lo >> 32) & 65535];
    x ^= MEMO[3][(lo >> 48) & 65535];
    x ^= MEMO[4][hi & 65535];
    x ^= MEMO[5][(hi >> 16) & 65535];
    x ^= MEMO[6][(hi >> 32) & 65535];
    x ^= MEMO[7][(hi >> 48) & 65535];
    return x;
  }

  u64 val;
  constexpr GF2(const u64 val = 0) noexcept : val(val & mask()) {}
  bool operator<(const GF2 &other) const {
    return val < other.val;
  } // To use std::map
  GF2 &operator+=(const GF2 &p) {
    val ^= p.val;
    return *this;
  }
  GF2 &operator-=(const GF2 &p) {
    val ^= p.val;
    return *this;
  }
  GF2 &operator*=(const GF2 &p) {
    val = mul(val, p.val);
    return *this;
  }

  GF2 &operator/=(const GF2 &p) {
    *this *= p.inverse();
    return *this;
  }
  GF2 operator-() const { return GF2(-val); }
  GF2 operator+(const GF2 &p) const { return GF2(*this) += p; }
  GF2 operator-(const GF2 &p) const { return GF2(*this) -= p; }
  GF2 operator*(const GF2 &p) const { return GF2(*this) *= p; }
  GF2 operator/(const GF2 &p) const { return GF2(*this) /= p; }
  bool operator==(const GF2 &p) const { return val == p.val; }
  bool operator!=(const GF2 &p) const { return val != p.val; }
  GF2 inverse() const { return pow((u64(1) << K) - 2); }
  GF2 pow(u64 n) const {
    GF2 ret(1), mul(val);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
};

#ifdef FASTIO
template <int K>
void rd(GF2<K> &x) {
  fastio::rd(x.val);
  x &= GF2<K>::mask;
}
template <int K>
void wt(GF2<K> x) {
  fastio::wt(x.val);
}
#endif
#line 1 "string/rollinghash_field.hpp"
// +, -, * が定義された構造体を渡す
template <typename Field>
struct RollingHash_Field {
  using F = Field;
  const F base;
  vector<F> power;

  static inline F generate_base() { return RNG(1LL << 60); }

  inline void expand(int sz) {
    if (int(power.size()) < sz + 1) {
      int pre_sz = (int)power.size();
      power.resize(sz + 1);
      for (int i = pre_sz - 1; i < sz; i++) { power[i + 1] = power[i] * base; }
    }
  }

  explicit RollingHash_Field(F base = generate_base()) : base(base), power{1} {}

  template <typename STRING>
  vector<F> build(const STRING &s) const {
    int sz = s.size();
    vector<F> hashed(sz + 1);
    for (int i = 0; i < sz; i++) {
      hashed[i + 1] = (hashed[i] * base) + F(s[i]);
    }
    return hashed;
  }

  F query(const vector<F> &s, int l, int r) {
    expand(r - l);
    return s[r] - s[l] * power[r - l];
  }

  F combine(F h1, F h2, size_t h2len) {
    expand(h2len);
    return add(mul(h1, power[h2len]), h2);
  }

  int lcp(const vector<F> &a, int l1, int r1, const vector<F> &b, int l2,
          int r2) {
    int len = min(r1 - l1, r2 - l2);
    int low = 0, high = len + 1;
    while (high - low > 1) {
      int mid = (low + high) / 2;
      if (query(a, l1, l1 + mid) == query(b, l2, l2 + mid))
        low = mid;
      else
        high = mid;
    }
    return low;
  }
};
#line 8 "test_atcoder/abc274_h.test.cpp"

void solve() {
  LL(N, Q);
  VEC(ll, A, N);
  using F = GF2<60>;
  RollingHash_Field<F> X;
  auto HA = X.build(A);

  FOR(Q) {
    LL(a, b, c, d, e, f);
    --a, --c, --e;
    ll n1 = b - a, n2 = f - e;

    auto check = [&](int n) -> bool {
      // lcp >= n
      if (n1 < n || n2 < n) return false;
      F x1 = X.query(HA, a, a + n);
      F x2 = X.query(HA, c, c + n);
      F x3 = X.query(HA, e, e + n);
      return (x1 + x2) == x3;
    };

    ll n = binary_search(check, 0, N + 1);
    if (n < min(n1, n2)) {
      u64 x = A[a + n] ^ A[c + n];
      u64 y = A[e + n];
      Yes(x < y);
    } else {
      // prefix
      Yes(n1 < n2);
    }
  }
}

signed main() {
  cout << fixed << setprecision(15);

  ll T = 1;
  // LL(T);
  FOR(T) solve();

  return 0;
}
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