#line 1 "ucup3-25/B/main.cpp"
#include <cstdint>
#define YOSUPO_AVX2_PRAGMA
// #undef YOSUPO_LOCAL

#line 2 "/home/vscode/yosupo-library/src/yosupo/fastio.hpp"

#include <unistd.h>
#include <algorithm>
#include <array>
#include <bit>
#include <cassert>
#include <cctype>
#line 10 "/home/vscode/yosupo-library/src/yosupo/fastio.hpp"
#include <cstring>
#include <sstream>
#include <string>
#include <type_traits>
#include <vector>

#line 2 "/home/vscode/yosupo-library/src/yosupo/internal_type_traits.hpp"

#line 5 "/home/vscode/yosupo-library/src/yosupo/internal_type_traits.hpp"

namespace yosupo {

namespace internal {

template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral =
    typename std::conditional<std::is_integral<T>::value ||
                                  internal::is_signed_int128<T>::value ||
                                  internal::is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

template <class T>
using is_integral_t = std::enable_if_t<is_integral<T>::value>;

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace yosupo
#line 17 "/home/vscode/yosupo-library/src/yosupo/fastio.hpp"

namespace yosupo {

struct Scanner {
  public:
    Scanner(const Scanner&) = delete;
    Scanner& operator=(const Scanner&) = delete;

    Scanner(FILE* fp) : fd(fileno(fp)) { line[0] = 127; }

    void read() {}
    template <class H, class... T> void read(H& h, T&... t) {
        bool f = read_single(h);
        assert(f);
        read(t...);
    }

    int read_unsafe() { return 0; }
    template <class H, class... T> int read_unsafe(H& h, T&... t) {
        bool f = read_single(h);
        if (!f) return 0;
        return 1 + read_unsafe(t...);
    }

    int close() { return ::close(fd); }

  private:
    static constexpr int SIZE = 1 << 15;

    int fd = -1;
    std::array<char, SIZE + 1> line;
    int st = 0, ed = 0;
    bool eof = false;

    bool read_single(std::string& ref) {
        if (!skip_space()) return false;
        ref = "";
        while (true) {
            char c = top();
            if (c <= ' ') break;
            ref += c;
            st++;
        }
        return true;
    }
    bool read_single(double& ref) {
        std::string s;
        if (!read_single(s)) return false;
        ref = std::stod(s);
        return true;
    }

    template <class T,
              std::enable_if_t<std::is_same<T, char>::value>* = nullptr>
    bool read_single(T& ref) {
        if (!skip_space<50>()) return false;
        ref = top();
        st++;
        return true;
    }

    template <class T,
              internal::is_signed_int_t<T>* = nullptr,
              std::enable_if_t<!std::is_same<T, char>::value>* = nullptr>
    bool read_single(T& sref) {
        using U = internal::to_unsigned_t<T>;
        if (!skip_space<50>()) return false;
        bool neg = false;
        if (line[st] == '-') {
            neg = true;
            st++;
        }
        U ref = 0;
        do {
            ref = 10 * ref + (line[st++] & 0x0f);
        } while (line[st] >= '0');
        sref = neg ? -ref : ref;
        return true;
    }
    template <class U,
              internal::is_unsigned_int_t<U>* = nullptr,
              std::enable_if_t<!std::is_same<U, char>::value>* = nullptr>
    bool read_single(U& ref) {
        if (!skip_space<50>()) return false;
        ref = 0;
        do {
            ref = 10 * ref + (line[st++] & 0x0f);
        } while (line[st] >= '0');
        return true;
    }

    bool reread() {
        if (ed - st >= 50) return true;
        if (st > SIZE / 2) {
            std::memmove(line.data(), line.data() + st, ed - st);
            ed -= st;
            st = 0;
        }
        if (eof) return false;
        auto u = ::read(fd, line.data() + ed, SIZE - ed);
        if (u == 0) {
            eof = true;
            line[ed] = '\0';
            u = 1;
        }
        ed += int(u);
        line[ed] = char(127);
        return true;
    }

    char top() {
        if (st == ed) {
            bool f = reread();
            assert(f);
        }
        return line[st];
    }

    template <int TOKEN_LEN = 0> bool skip_space() {
        while (true) {
            while (line[st] <= ' ') st++;
            if (ed - st > TOKEN_LEN) return true;
            if (st > ed) st = ed;
            for (auto i = st; i < ed; i++) {
                if (line[i] <= ' ') return true;
            }
            if (!reread()) return false;
        }
    }
};

struct Printer {
  public:
    template <char sep = ' ', bool F = false> void write() {}
    template <char sep = ' ', bool F = false, class H, class... T>
    void write(const H& h, const T&... t) {
        if (F) write_single(sep);
        write_single(h);
        write<true>(t...);
    }
    template <char sep = ' ', class... T> void writeln(const T&... t) {
        write<sep>(t...);
        write_single('\n');
    }

    Printer(FILE* _fp) : fd(fileno(_fp)) {}
    ~Printer() { flush(); }

    int close() {
        flush();
        return ::close(fd);
    }

    void flush() {
        if (pos) {
            auto res = ::write(fd, line.data(), pos);
            assert(res != -1);
            pos = 0;
        }
    }

  private:
    static std::array<std::array<char, 2>, 100> small;
    static std::array<unsigned long long, 20> tens;

    static constexpr size_t SIZE = 1 << 15;
    int fd;
    std::array<char, SIZE> line;
    size_t pos = 0;
    std::stringstream ss;

    template <class T,
              std::enable_if_t<std::is_same<char, T>::value>* = nullptr>
    void write_single(const T& val) {
        if (pos == SIZE) flush();
        line[pos++] = val;
    }

    template <class T,
              internal::is_signed_int_t<T>* = nullptr,
              std::enable_if_t<!std::is_same<char, T>::value>* = nullptr>
    void write_single(const T& val) {
        using U = internal::to_unsigned_t<T>;
        if (val == 0) {
            write_single('0');
            return;
        }
        if (pos > SIZE - 50) flush();
        U uval = val;
        if (val < 0) {
            write_single('-');
            uval = -uval;
        }
        write_unsigned(uval);
    }

    template <class U,
              internal::is_unsigned_int_t<U>* = nullptr,
              std::enable_if_t<!std::is_same<char, U>::value>* = nullptr>
    void write_single(U uval) {
        if (uval == 0) {
            write_single('0');
            return;
        }
        if (pos > SIZE - 50) flush();

        write_unsigned(uval);
    }

    static int calc_len(uint64_t x) {
        int i = ((63 - std::countl_zero(x)) * 3 + 3) / 10;
        if (x < tens[i])
            return i;
        else
            return i + 1;
    }

    template <class U,
              internal::is_unsigned_int_t<U>* = nullptr,
              std::enable_if_t<2 >= sizeof(U)>* = nullptr>
    void write_unsigned(U uval) {
        size_t len = calc_len(uval);
        pos += len;

        char* ptr = line.data() + pos;
        while (uval >= 100) {
            ptr -= 2;
            memcpy(ptr, small[uval % 100].data(), 2);
            uval /= 100;
        }
        if (uval >= 10) {
            memcpy(ptr - 2, small[uval].data(), 2);
        } else {
            *(ptr - 1) = char('0' + uval);
        }
    }

    template <class U,
              internal::is_unsigned_int_t<U>* = nullptr,
              std::enable_if_t<4 == sizeof(U)>* = nullptr>
    void write_unsigned(U uval) {
        std::array<char, 8> buf;
        memcpy(buf.data() + 6, small[uval % 100].data(), 2);
        memcpy(buf.data() + 4, small[uval / 100 % 100].data(), 2);
        memcpy(buf.data() + 2, small[uval / 10000 % 100].data(), 2);
        memcpy(buf.data() + 0, small[uval / 1000000 % 100].data(), 2);

        if (uval >= 100000000) {
            if (uval >= 1000000000) {
                memcpy(line.data() + pos, small[uval / 100000000 % 100].data(),
                       2);
                pos += 2;
            } else {
                line[pos] = char('0' + uval / 100000000);
                pos++;
            }
            memcpy(line.data() + pos, buf.data(), 8);
            pos += 8;
        } else {
            size_t len = calc_len(uval);
            memcpy(line.data() + pos, buf.data() + (8 - len), len);
            pos += len;
        }
    }

    template <class U,
              internal::is_unsigned_int_t<U>* = nullptr,
              std::enable_if_t<8 == sizeof(U)>* = nullptr>
    void write_unsigned(U uval) {
        size_t len = calc_len(uval);
        pos += len;

        char* ptr = line.data() + pos;
        while (uval >= 100) {
            ptr -= 2;
            memcpy(ptr, small[uval % 100].data(), 2);
            uval /= 100;
        }
        if (uval >= 10) {
            memcpy(ptr - 2, small[uval].data(), 2);
        } else {
            *(ptr - 1) = char('0' + uval);
        }
    }

    template <
        class U,
        std::enable_if_t<internal::is_unsigned_int128<U>::value>* = nullptr>
    void write_unsigned(U uval) {
        static std::array<char, 50> buf;
        size_t len = 0;
        while (uval > 0) {
            buf[len++] = char((uval % 10) + '0');
            uval /= 10;
        }
        std::reverse(buf.begin(), buf.begin() + len);
        memcpy(line.data() + pos, buf.data(), len);
        pos += len;
    }

    void write_single(const std::string& s) {
        for (char c : s) write_single(c);
    }
    void write_single(const char* s) {
        size_t len = strlen(s);
        for (size_t i = 0; i < len; i++) write_single(s[i]);
    }
    template <class T> void write_single(const std::vector<T>& val) {
        auto n = val.size();
        for (size_t i = 0; i < n; i++) {
            if (i) write_single(' ');
            write_single(val[i]);
        }
    }
};

inline std::array<std::array<char, 2>, 100> Printer::small = [] {
    std::array<std::array<char, 2>, 100> table;
    for (int i = 0; i <= 99; i++) {
        table[i][1] = char('0' + (i % 10));
        table[i][0] = char('0' + (i / 10 % 10));
    }
    return table;
}();
inline std::array<unsigned long long, 20> Printer::tens = [] {
    std::array<unsigned long long, 20> table;
    for (int i = 0; i < 20; i++) {
        table[i] = 1;
        for (int j = 0; j < i; j++) {
            table[i] *= 10;
        }
    }
    return table;
}();

}  // namespace yosupo
#line 2 "/home/vscode/yosupo-library/src/yosupo/fastset.hpp"

#line 8 "/home/vscode/yosupo-library/src/yosupo/fastset.hpp"

namespace yosupo {

struct FastSet {
    static constexpr int B = 64;

    // bool配列a_0, a_1, ..., a_nを作る
    explicit FastSet(int n) : _n(n) {
        do {
            seg.push_back(std::vector<uint64_t>((n + B - 1) / B));
            n = (n + B - 1) / B;
        } while (n > 1);
        _log = int(seg.size());
    }

    // bool配列a_0, a_1, ..., a_nを作る
    explicit FastSet(int n, std::vector<uint64_t> v) : _n(n) {
        {
            int n2 = (n + B - 1) / B;
            seg.push_back(v); //std::vector<uint64_t>(n2));
            // for (int i = 0; i < n; i++) {
            //     if (v[i]) seg[0][i / B] |= 1ULL << (i % B);
            // }
            n = n2;
        }
        while (n > 1) {
            int n2 = (n + B - 1) / B;
            std::vector<uint64_t> v2(n2);
            for (int i = 0; i < n; i++) {
                if (seg.back()[i]) {
                    v2[i / B] |= 1ULL << (i % B);
                }
            }
            seg.push_back(std::move(v2));
            n = n2;
        }
        _log = int(seg.size());
    }

    // a[i]を返す。a[i] = falseは出来ないことに注意(要検討)
    bool operator[](int i) const { return (seg[0][i / B] >> (i % B) & 1) != 0; }

    // a[i] = true
    void set(int i) {
        for (int h = 0; h < _log; h++) {
            seg[h][i / B] |= 1ULL << (i % B);
            i /= B;
        }
    }

    // a[i] = false
    void reset(int i) {
        for (int h = 0; h < _log; h++) {
            seg[h][i / B] &= ~(1ULL << (i % B));
            if (seg[h][i / B]) break;
            i /= B;
        }
    }

    // @return i以上最小の要素 or n
    int or_more(int i) const {
        if (i >= _n) return _n;
        i = std::max(i, 0);
        for (int h = 0; h < _log; h++) {
            if (i / B == int(seg[h].size())) break;
            uint64_t d = seg[h][i / B] >> (i % B);
            if (!d) {
                i = i / B + 1;
                continue;
            }
            // find
            i += std::countr_zero(d);
            for (int g = h - 1; g >= 0; g--) {
                i *= B;
                i += std::countr_zero(seg[g][i / B]);
            }
            assert((*this)[i]);
            return i;
        }
        return _n;
    }

    // @return iより大きい最小の要素 or n
    int more(int i) const {
        if (i >= _n - 1) return _n;
        return or_more(i + 1);
    }

    // @return i以下最大の要素 or -1
    int or_less(int i) const {
        if (i < 0) return -1;
        i = std::min(i, _n - 1);
        for (int h = 0; h < _log; h++) {
            if (i == -1) break;
            uint64_t d = seg[h][i / B] << (63 - i % 64);
            if (!d) {
                i = i / B - 1;
                continue;
            }
            // find
            i -= std::countl_zero(d);
            for (int g = h - 1; g >= 0; g--) {
                i *= B;
                i += B - 1 - std::countl_zero(seg[g][i / B]);
            }
            return i;
        }
        return -1;
    }

    // @return iより小さい最大の要素 or -1
    int less(int i) const {
        if (i <= 0) return -1;
        return or_less(i - 1);
    }

  private:
    int _n, _log;
    std::vector<std::vector<uint64_t>> seg;
};

}  // namespace yosupo
#line 2 "/home/vscode/yosupo-library/src/yosupo/random.hpp"

#line 6 "/home/vscode/yosupo-library/src/yosupo/random.hpp"
#include <chrono>
#line 8 "/home/vscode/yosupo-library/src/yosupo/random.hpp"
#include <random>
#line 10 "/home/vscode/yosupo-library/src/yosupo/random.hpp"

namespace yosupo {

struct Xoshiro256StarStar {
  public:
    using result_type = uint64_t;
    Xoshiro256StarStar() : Xoshiro256StarStar(0) {}
    explicit Xoshiro256StarStar(uint64_t seed) {
        // use splitmix64
        // Reference: http://xoshiro.di.unimi.it/splitmix64.c
        for (int i = 0; i < 4; i++) {
            uint64_t z = (seed += 0x9e3779b97f4a7c15);
            z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9;
            z = (z ^ (z >> 27)) * 0x94d049bb133111eb;
            s[i] = z ^ (z >> 31);
        }
    }

    static constexpr result_type min() { return 0; }
    static constexpr result_type max() { return -1; }

    result_type operator()() {
        const uint64_t result_starstar = rotl(s[1] * 5, 7) * 9;

        const uint64_t t = s[1] << 17;

        s[2] ^= s[0];
        s[3] ^= s[1];
        s[1] ^= s[2];
        s[0] ^= s[3];

        s[2] ^= t;

        s[3] = rotl(s[3], 45);

        return result_starstar;
    }

  private:
    // Use xoshiro256**
    // Refereces: http://xoshiro.di.unimi.it/xoshiro256starstar.c
    static uint64_t rotl(const uint64_t x, int k) {
        return (x << k) | (x >> (64 - k));
    }

    std::array<uint64_t, 4> s;
};

// https://github.com/wangyi-fudan/wyhash
struct WYRand {
  public:
    using result_type = uint64_t;
    explicit WYRand(uint64_t seed) : s(seed) {}

    static constexpr result_type min() { return 0; }
    static constexpr result_type max() { return -1; }

    result_type operator()() {
        s += 0x2d358dccaa6c78a5;
        auto x = (unsigned __int128)s * (s ^ 0x8bb84b93962eacc9);
        return (uint64_t)(x ^ (x >> 64));
    }

  private:
    uint64_t s;
};
using Random = WYRand;
inline Random& global_gen() {
    static Random gen(
        std::chrono::steady_clock::now().time_since_epoch().count());
    return gen;
}

template <class G>
concept random_64 = std::uniform_random_bit_generator<G> &&
                    std::same_as<uint64_t, std::invoke_result_t<G&>> &&
                    G::min() == uint64_t(0) && G::max() == uint64_t(-1);

namespace internal {

// random choice from [0, upper]
template <random_64 G> uint64_t uniform_u64(uint64_t upper, G& gen) {
    if (!(upper & (upper + 1))) {
        // b = 00..0011..11
        return gen() & upper;
    }
    int log = 63 - std::countl_zero(upper);
    uint64_t mask = (log == 63) ? ~0ULL : (1ULL << (log + 1)) - 1;
    while (true) {
        uint64_t r = gen() & mask;
        if (r <= upper) return r;
    }
}

// random choice from [0, upper], faster than uniform_u64
template <random_64 G> uint64_t random_u64(uint64_t upper, G& gen) {
    return (uint64_t)(((unsigned __int128)(upper) + 1) * gen() >> 64);
}

}  // namespace internal

template <class T, random_64 G> T uniform(T lower, T upper, G& gen) {
    return T(lower +
             internal::uniform_u64(uint64_t(upper) - uint64_t(lower), gen));
}
template <class T> T uniform(T lower, T upper) {
    return uniform(lower, upper, global_gen());
}
template <class T, random_64 G> T random(T lower, T upper, G& gen) {
    return T(lower +
             internal::random_u64(uint64_t(upper) - uint64_t(lower), gen));
}
template <class T> T random(T lower, T upper) {
    return random(lower, upper, global_gen());
}

template <random_64 G> bool uniform_bool(G& gen) { return gen() & 1; }
inline bool uniform_bool() { return uniform_bool(global_gen()); }

// select 2 elements from [lower, uppper]
template <class T, random_64 G>
std::pair<T, T> uniform_pair(T lower, T upper, G& gen) {
    assert(upper - lower >= 1);
    T a, b;
    do {
        a = uniform(lower, upper, gen);
        b = uniform(lower, upper, gen);
    } while (a == b);
    if (a > b) std::swap(a, b);
    return {a, b};
}
template <class T> std::pair<T, T> uniform_pair(T lower, T upper) {
    return uniform_pair(lower, upper, global_gen());
}

// random value in the interval (0.0, 1.0]
template <class G> inline double open_closed_01(G& gen) {
    union {
        uint64_t i;
        double f;
    } u = {0xbff0000000000000 | (gen() >> 12)};
    return 2.0 + u.f;
}
inline double open_closed_01() {
    return open_closed_01(global_gen());
}

}  // namespace yosupo
#line 8 "ucup3-25/B/main.cpp"
using namespace yosupo;

#line 2 "ucup3-25/B/base.hpp"

#ifdef YOSUPO_AVX2_PRAGMA
#line 5 "ucup3-25/B/base.hpp"
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#endif

#line 11 "ucup3-25/B/base.hpp"
#include <bitset>
#line 13 "ucup3-25/B/base.hpp"
#include <cmath>
#include <cstdio>
#line 16 "ucup3-25/B/base.hpp"
#include <iostream>
#include <map>
#include <queue>
#include <ranges>
#include <set>
#line 22 "ucup3-25/B/base.hpp"
#include <utility>
#line 24 "ucup3-25/B/base.hpp"

using std::abs, std::pow, std::sqrt;
using std::array, std::vector, std::string, std::queue, std::deque;
using std::countl_zero, std::countl_one, std::countr_zero, std::countr_one;
using std::istream, std::ostream, std::cerr, std::endl;
using std::min, std::max, std::swap;
using std::pair, std::tuple, std::bitset;
using std::popcount;
using std::priority_queue, std::set, std::multiset, std::map;
using std::views::iota, std::views::reverse;

namespace ranges = std::ranges;
using ranges::sort, ranges::copy_n;

using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;

#ifdef YOSUPO_LOCAL

inline ostream& operator<<(ostream& os, __int128_t x) {
    if (x < 0) {
        os << "-";
        x *= -1;
    }
    if (x == 0) {
        return os << "0";
    }
    string s;
    while (x) {
        s += char(x % 10 + '0');
        x /= 10;
    }
    ranges::reverse(s);
    return os << s;
}
inline ostream& operator<<(ostream& os, __uint128_t x) {
    if (x == 0) {
        return os << "0";
    }
    string s;
    while (x) {
        s += char(x % 10 + '0');
        x /= 10;
    }
    ranges::reverse(s);
    return os << s;
}

template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p);
template <class T> ostream& operator<<(ostream& os, const V<T>& v);
template <class T> ostream& operator<<(ostream& os, const deque<T>& v);
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a);
template <class T> ostream& operator<<(ostream& os, const set<T>& s);
template <class T, class U>
ostream& operator<<(ostream& os, const map<T, U>& m);

template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    return os << "P(" << p.first << ", " << p.second << ")";
}

template <class T> ostream& operator<<(ostream& os, const V<T>& v) {
    os << "[";
    bool f = false;
    for (auto d : v) {
        if (f) os << ", ";
        f = true;
        os << d;
    }
    return os << "]";
}

template <class T> ostream& operator<<(ostream& os, const deque<T>& v) {
    os << "[";
    bool f = false;
    for (auto d : v) {
        if (f) os << ", ";
        f = true;
        os << d;
    }
    return os << "]";
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a) {
    os << "[";
    bool f = false;
    for (auto d : a) {
        if (f) os << ", ";
        f = true;
        os << d;
    }
    return os << "]";
}

template <class T> ostream& operator<<(ostream& os, const set<T>& s) {
    os << "{";
    bool f = false;
    for (auto d : s) {
        if (f) os << ", ";
        f = true;
        os << d;
    }
    return os << "}";
}
template <class T> ostream& operator<<(ostream& os, const multiset<T>& s) {
    os << "{";
    bool f = false;
    for (auto d : s) {
        if (f) os << ", ";
        f = true;
        os << d;
    }
    return os << "}";
}

template <class T, class U>
ostream& operator<<(ostream& os, const map<T, U>& s) {
    os << "{";
    bool f = false;
    for (auto p : s) {
        if (f) os << ", ";
        f = true;
        os << p.first << ": " << p.second;
    }
    return os << "}";
}

struct PrettyOS {
    ostream& os;
    bool first;

    template <class T> auto operator<<(T&& x) {
        if (!first) os << ", ";
        first = false;
        os << x;
        return *this;
    }
};
template <class... T> void dbg0(T&&... t) {
    (PrettyOS{cerr, true} << ... << t);
}
#define dbg(...)                                            \
    do {                                                    \
        cerr << __LINE__ << " : " << #__VA_ARGS__ << " = "; \
        dbg0(__VA_ARGS__);                                  \
        cerr << endl;                                       \
    } while (false);
#else
#define dbg(...)
#endif
#line 11 "ucup3-25/B/main.cpp"

Scanner sc = Scanner(stdin);
Printer pr = Printer(stdout);

int main() {
    int n, q;
    sc.read(n, q);
    //n = TEN(6);
    //q = TEN(6);

    // 01-reversed
    V<FastSet> s0, s1;
    auto set = [&](int i, ull x) {
        for (int j : iota(0, 63)) {
            if ((x >> j) & 1) {
                s0[j].reset(i);
                s1[j].set(i);
            } else {
                s0[j].set(i);
                s1[j].reset(i);
            }
        }
    };

    if (true) {
        int n2 = (n + 63) / 64;
        VV<uint64_t> v0(63, V<uint64_t>(n2));
        VV<uint64_t> v1(63, V<uint64_t>(n2));
        for (int i : iota(0, n)) {
            ull x;
            sc.read(x);
            //x = uniform(0ULL, -1ULL);
            for (int j : iota(0, 63)) {
                if ((x >> j) & 1) {
                    v1[j][i / 64] |= 1ULL << (i % 64);  
                } else {
                    v0[j][i / 64] |= 1ULL << (i % 64);
                }
            }
        }

        for (int i : iota(0, 63)) {
            s0.emplace_back(n, std::move(v0[i]));
            s1.emplace_back(n, std::move(v1[i]));
        }
    } else {
        for (int _ : iota(0, 63)) {
            s0.emplace_back(n);
            s1.emplace_back(n);
        }
        for (int i : iota(0, n)) {
            ull x = uniform(0ULL, -1ULL);
            set(i, x);
        }
    }
 
    for (int _ : iota(0, q)) {
        int t;
        sc.read(t);
        //t = uniform(1, 3);

        if (t == 1) {
            int l, r;
            ull x;
            sc.read(l, r, x);
            l--;

            //std::tie(l, r) = uniform_pair(0, n);
            //x = uniform(0ULL, -1ULL);

            for (int j : iota(0, 63)) {
                if ((x >> j) & 1) continue;
                int i = l;
                while (true) {
                    i = s1[j].or_more(i);
                    if (i >= r) break;
                    s1[j].reset(i);
                    s0[j].set(i);
                }
            }
        } else if (t == 2) {
            int i;
            ull x;            
            sc.read(i, x);
            i--;

            //i = uniform(0, n - 1);
            //x = uniform(0ULL, -1ULL);
            // x = -1ULL;

            set(i, x);
        } else if (t == 3) {
            int l, r;
            sc.read(l, r);
            l--;

            //std::tie(l, r) = uniform_pair(0, n);

            ull ans = 0;
            int p = -1;
            for (int j : iota(0, 63) | reverse) {
                ans <<= 1;

                int i0 = s0[j].or_more(l);
                if (i0 >= r) {
                    // all 1
                    ans |= 1;
                    continue;
                }
                if (p != -1 && p != i0) {
                    // different 0
                    continue;
                }
                int i1 = s0[j].more(i0);
                if (i1 < r) {
                    // two 0s
                    continue;
                }
                p = i0;
                ans |= 1;
            }

            pr.writeln(ans);
        } else {
            assert(false);
        }
    }
    return 0;
}