#line 1 "main.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1332"
#line 1 "library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;

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); }
// (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, typename U>
T ceil(T x, U y) {
  return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
  return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

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

#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) {
  assert(!que.empty());
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  assert(!que.empty());
  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;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, 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;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, 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 "library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>

namespace fastio {
#define FASTIO
// クラスが read(), print() を持っているかを判定するメタ関数
struct has_write_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.write(), std::true_type{});

  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_write : public decltype(has_write_impl::check<T>(std::declval<T>())) {
};

struct has_read_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.read(), std::true_type{});

  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_read : public decltype(has_read_impl::check<T>(std::declval<T>())) {};

struct Scanner {
  FILE *fp;
  char line[(1 << 15) + 1];
  size_t st = 0, ed = 0;
  void reread() {
    memmove(line, line + st, ed - st);
    ed -= st;
    st = 0;
    ed += fread(line + ed, 1, (1 << 15) - ed, fp);
    line[ed] = '\0';
  }
  bool succ() {
    while (true) {
      if (st == ed) {
        reread();
        if (st == ed) return false;
      }
      while (st != ed && isspace(line[st])) st++;
      if (st != ed) break;
    }
    if (ed - st <= 50) {
      bool sep = false;
      for (size_t i = st; i < ed; i++) {
        if (isspace(line[i])) {
          sep = true;
          break;
        }
      }
      if (!sep) reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    while (true) {
      size_t sz = 0;
      while (st + sz < ed && !isspace(line[st + sz])) sz++;
      ref.append(line + st, sz);
      st += sz;
      if (!sz || st != ed) break;
      reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    bool neg = false;
    if (line[st] == '-') {
      neg = true;
      st++;
    }
    ref = T(0);
    while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
    if (neg) ref = -ref;
    return true;
  }
  template <typename T,
            typename enable_if<has_read<T>::value>::type * = nullptr>
  inline bool read_single(T &x) {
    x.read();
    return true;
  }
  bool read_single(double &ref) {
    string s;
    if (!read_single(s)) return false;
    ref = std::stod(s);
    return true;
  }
  bool read_single(char &ref) {
    string s;
    if (!read_single(s) || s.size() != 1) return false;
    ref = s[0];
    return true;
  }
  template <class T>
  bool read_single(vector<T> &ref) {
    for (auto &d: ref) {
      if (!read_single(d)) return false;
    }
    return true;
  }
  template <class T, class U>
  bool read_single(pair<T, U> &p) {
    return (read_single(p.first) && read_single(p.second));
  }
  template <size_t N = 0, typename T>
  void read_single_tuple(T &t) {
    if constexpr (N < std::tuple_size<T>::value) {
      auto &x = std::get<N>(t);
      read_single(x);
      read_single_tuple<N + 1>(t);
    }
  }
  template <class... T>
  bool read_single(tuple<T...> &tpl) {
    read_single_tuple(tpl);
    return true;
  }
  void read() {}
  template <class H, class... T>
  void read(H &h, T &... t) {
    bool f = read_single(h);
    assert(f);
    read(t...);
  }
  Scanner(FILE *fp) : fp(fp) {}
};

struct Printer {
  Printer(FILE *_fp) : fp(_fp) {}
  ~Printer() { flush(); }

  static constexpr size_t SIZE = 1 << 15;
  FILE *fp;
  char line[SIZE], small[50];
  size_t pos = 0;
  void flush() {
    fwrite(line, 1, pos, fp);
    pos = 0;
  }
  void write(const char val) {
    if (pos == SIZE) flush();
    line[pos++] = val;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  void write(T val) {
    if (pos > (1 << 15) - 50) flush();
    if (val == 0) {
      write('0');
      return;
    }
    if (val < 0) {
      write('-');
      val = -val; // todo min
    }
    size_t len = 0;
    while (val) {
      small[len++] = char(0x30 | (val % 10));
      val /= 10;
    }
    for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
    pos += len;
  }
  void write(const string s) {
    for (char c: s) write(c);
  }
  void write(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++) write(s[i]);
  }
  void write(const double x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  void write(const long double x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  template <typename T,
            typename enable_if<has_write<T>::value>::type * = nullptr>
  inline void write(T x) {
    x.write();
  }
  template <class T>
  void write(const vector<T> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  template <class T, class U>
  void write(const pair<T, U> val) {
    write(val.first);
    write(' ');
    write(val.second);
  }
  template <size_t N = 0, typename T>
  void write_tuple(const T t) {
    if constexpr (N < std::tuple_size<T>::value) {
      if constexpr (N > 0) { write(' '); }
      const auto x = std::get<N>(t);
      write(x);
      write_tuple<N + 1>(t);
    }
  }
  template <class... T>
  bool write(tuple<T...> tpl) {
    write_tuple(tpl);
    return true;
  }
  template <class T, size_t S>
  void write(const array<T, S> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  void write(i128 val) {
    string s;
    bool negative = 0;
    if (val < 0) {
      negative = 1;
      val = -val;
    }
    while (val) {
      s += '0' + int(val % 10);
      val /= 10;
    }
    if (negative) s += "-";
    reverse(all(s));
    if (len(s) == 0) s = "0";
    write(s);
  }
};
Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);
void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  printer.write(head);
  if (sizeof...(Tail)) printer.write(' ');
  print(forward<Tail>(tail)...);
}

void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
  scanner.read(head);
  read(tail...);
}
} // namespace fastio
using fastio::print;
using fastio::flush;
using fastio::read;

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __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 1 "library/ds/bit_vector.hpp"
struct Bit_Vector {
  vc<pair<u32, u32>> dat;
  Bit_Vector(int n) { dat.assign((n + 63) >> 5, {0, 0}); }

  void set(int i) { dat[i >> 5].fi |= u32(1) << (i & 31); }

  void build() {
    FOR(i, len(dat) - 1) dat[i + 1].se = dat[i].se + popcnt(dat[i].fi);
  }

  // [0, k) 内の 1 の個数
  int rank(int k, bool f = 1) {
    auto [a, b] = dat[k >> 5];
    int ret = b + popcnt(a & ((u32(1) << (k & 31)) - 1));
    return (f ? ret : k - ret);
  }
};
#line 2 "library/alg/monoid/add.hpp"

template <typename X>
struct Monoid_Add {
  using value_type = X;
  static constexpr X op(const X &x, const X &y) noexcept { return x + y; }
  static constexpr X inverse(const X &x) noexcept { return -x; }
  static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; }
  static constexpr X unit() { return X(0); }
  static constexpr bool commute = true;
};
#line 3 "library/ds/wavelet_matrix.hpp"

// 座圧するかどうかを COMPRESS で指定する
// xor 的な使い方をする場合には、コンストラクタで log を渡すこと
template <typename T, bool COMPRESS, typename Monoid = Monoid_Add<T>>
struct Wavelet_Matrix {
  using MX = Monoid;
  using X = typename MX::value_type;
  static_assert(MX::commute);
  int N, lg;
  vector<int> mid;
  vector<Bit_Vector> bv;
  vc<T> key;
  const bool set_log;
  vvc<X> cumsum;

  // 和を使わないなら、SUM_data は空でよい
  Wavelet_Matrix(vc<T> A, vc<X> SUM_data = {}, int log = -1)
      : N(len(A)), lg(log), set_log(log != -1) {
    bool MAKE_SUM = !(SUM_data.empty());
    vc<X>& S = SUM_data;
    if (COMPRESS) {
      assert(!set_log);
      key.reserve(N);
      vc<int> I = argsort(A);
      for (auto&& i: I) {
        if (key.empty() || key.back() != A[i]) key.eb(A[i]);
        A[i] = len(key) - 1;
      }
      key.shrink_to_fit();
    }
    if (lg == -1) lg = __lg(max<ll>(MAX(A), 1)) + 1;
    mid.resize(lg);
    bv.assign(lg, Bit_Vector(N));
    if (MAKE_SUM) cumsum.assign(1 + lg, vc<X>(N + 1, MX::unit()));
    vc<T> A0(N), A1(N);
    vc<X> S0(N), S1(N);
    FOR_R(d, -1, lg) {
      int p0 = 0, p1 = 0;
      if (MAKE_SUM) {
        FOR(i, N) { cumsum[d + 1][i + 1] = MX::op(cumsum[d + 1][i], S[i]); }
      }
      if (d == -1) break;
      FOR(i, N) {
        bool f = (A[i] >> d & 1);
        if (!f) {
          if (MAKE_SUM) S0[p0] = S[i];
          A0[p0++] = A[i];
        }
        if (f) {
          if (MAKE_SUM) S1[p1] = S[i];
          bv[d].set(i), A1[p1++] = A[i];
        }
      }
      mid[d] = p0;
      bv[d].build();
      swap(A, A0), swap(S, S0);
      FOR(i, p1) A[p0 + i] = A1[i], S[p0 + i] = S1[i];
    }
  }

  // xor した結果で [a, b) に収まるものを数える
  int count(int L, int R, T a, T b, T xor_val = 0) {
    return prefix_count(L, R, b, xor_val) - prefix_count(L, R, a, xor_val);
  }

  // xor した結果で、[L, R) の中で k>=0 番目
  T kth(int L, int R, int k, T xor_val = 0) {
    if (xor_val != 0) assert(set_log);
    assert(0 <= k && k < R - L);
    T ret = 0;
    for (int d = lg - 1; d >= 0; --d) {
      bool f = (xor_val >> d) & 1;
      int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
      int kf = (f ? (R - L) - (r0 - l0) : (r0 - l0));
      if (k < kf) {
        if (!f) L = l0, R = r0;
        if (f) L += mid[d] - l0, R += mid[d] - r0;
      } else {
        k -= kf, ret |= T(1) << d;
        if (!f) L += mid[d] - l0, R += mid[d] - r0;
        if (f) L = l0, R = r0;
      }
    }
    if (COMPRESS) ret = key[ret];
    return ret;
  }

  // xor した結果で、[L, R) の中で k>=0 番目と prefix sum
  pair<int, T> kth_value_and_sum(int L, int R, int k, T xor_val = 0) {
    if (xor_val != 0) assert(set_log);
    assert(0 <= k && k <= R - L);
    if (k == R - L) { return {infty<T>, sum_all(L, R)}; }
    T ret = 0;
    X sm = MX::unit();
    for (int d = lg - 1; d >= 0; --d) {
      bool f = (xor_val >> d) & 1;
      int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
      int kf = (f ? (R - L) - (r0 - l0) : (r0 - l0));
      if (k < kf) {
        if (!f) L = l0, R = r0;
        if (f) L += mid[d] - l0, R += mid[d] - r0;
      } else {
        X s = (f ? get(d, L + mid[d] - l0, R + mid[d] - r0) : get(d, l0, r0));
        k -= kf, ret |= T(1) << d, sm = MX::op(sm, s);
        if (!f) L += mid[d] - l0, R += mid[d] - r0;
        if (f) L = l0, R = r0;
      }
    }
    if (k) sm = MX::op(sm, get(0, L, L + k));
    if (COMPRESS) ret = key[ret];
    return {ret, sm};
  }

  // xor した結果で、[L, R) の中で中央値。
  // LOWER = true：下側中央値、false：上側中央値
  T median(bool UPPER, int L, int R, T xor_val = 0) {
    int n = R - L;
    int k = (UPPER ? n / 2 : (n - 1) / 2);
    return kth(L, R, k, xor_val);
  }

  // xor した結果で [k1, k2) 番目であるところの SUM_data の和
  X sum(int L, int R, int k1, int k2, T xor_val = 0) {
    return prefix_sum(L, R, k2, xor_val) - prefix_sum(L, R, k1, xor_val);
  }

  X sum_all(int L, int R) {
    return MX::op(MX::inverse(cumsum[lg][L]), cumsum[lg][R]);
  }

  // check(cnt, prefix sum) が true となるような最大個数
  template <typename F>
  int max_right(F check, int L, int R, T xor_val = 0) {
    assert(check(0, MX::unit()));
    if (xor_val != 0) assert(set_log);
    if (check(R - L, get(lg, L, R))) return R - L;
    int cnt = 0;
    X sm = MX::unit();
    for (int d = lg - 1; d >= 0; --d) {
      bool f = (xor_val >> d) & 1;
      int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
      int c = (f ? (R - L) - (r0 - l0) : (r0 - l0));
      X s = (f ? get(d, L + mid[d] - l0, R + mid[d] - r0) : get(d, l0, r0));
      if (check(cnt + c, MX::op(sm, s))) {
        cnt += c, sm = MX::op(sm, s);
        if (f) L = l0, R = r0;
        if (!f) L += mid[d] - l0, R += mid[d] - r0;
      } else {
        if (!f) L = l0, R = r0;
        if (f) L += mid[d] - l0, R += mid[d] - r0;
      }
    }
    cnt += binary_search(
        [&](int k) -> bool {
          return check(cnt + k, MX::op(sm, get(0, L, L + k)));
        },
        0, R - L);
    return cnt;
  }

private:
  inline X get(int d, int L, int R) {
    return MX::op(MX::inverse(cumsum[d][L]), cumsum[d][R]);
  }

  // xor した結果で [0, x) に収まるものを数える
  int prefix_count(int L, int R, T x, T xor_val = 0) {
    if (xor_val != 0) assert(set_log);
    x = (COMPRESS ? LB(key, x) : x);
    if (x == 0) return 0;
    if (x >= (1 << lg)) return R - L;
    int cnt = 0;
    FOR_R(d, lg) {
      bool add = (x >> d) & 1;
      bool f = ((xor_val) >> d) & 1;
      int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
      int kf = (f ? (R - L) - (r0 - l0) : (r0 - l0));
      if (add) {
        cnt += kf;
        if (f) { L = l0, R = r0; }
        if (!f) { L += mid[d] - l0, R += mid[d] - r0; }
      } else {
        if (!f) L = l0, R = r0;
        if (f) L += mid[d] - l0, R += mid[d] - r0;
      }
    }
    return cnt;
  }

  // xor した結果で [0, k) 番目のものの和
  X prefix_sum(int L, int R, int k, T xor_val = 0) {
    if (xor_val != 0) assert(set_log);
    assert(0 <= k && k <= R - L);
    if (k == 0) return MX::unit();
    if (k == R - L) return sum_all(L, R);
    assert(!cumsum.empty());

    X sm = MX::unit();
    for (int d = lg - 1; d >= 0; --d) {
      bool f = (xor_val >> d) & 1;
      int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
      int c = (f ? (R - L) - (r0 - l0) : (r0 - l0));
      X s = (f ? get(d, L + mid[d] - l0, R + mid[d] - r0) : get(d, l0, r0));
      if (k < c) {
        if (!f) L = l0, R = r0;
        if (f) L += mid[d] - l0, R += mid[d] - r0;
      } else {
        k -= c, sm = MX::op(sm, s);
        if (f) { L = l0, R = r0; }
        if (!f) { L += mid[d] - l0, R += mid[d] - r0; }
      }
    }
    if (k) sm = MX::op(sm, get(0, L, L + k));
    return sm;
  }
};
#line 5 "main.cpp"

void solve() {
  LL(N);
  VEC(ll, X, N);
  Wavelet_Matrix<ll, true> WM(X);
  LL(Q);
  FOR(Q) {
    LL(l, r, x);
    --l;
    ll ANS = infty<ll>;
    ll n = WM.count(l, r, 0, x);
    if (n > 0) chmin(ANS, abs(x - WM.kth(l, r, n - 1)));
    if (n < r - l) chmin(ANS, abs(x - WM.kth(l, r, n)));
    print(ANS);
  }
}

signed main() {
  solve();
  return 0;
}