#403352 (C++14) No.803 Very Limited Xor Subset

提出ソース

結果

問題	No.803 Very Limited Xor Subset
ユーザー	jell
提出日時	2019-11-30 22:30:28
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	7 ms / 2,000 ms
コード長	23,596 bytes
コンパイル時間	2,047 ms
コンパイル使用メモリ	188,488 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-05-01 03:20:10
合計ジャッジ時間	3,413 ms
ジャッジサーバーID （参考情報）	judge5 / judge2

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 6,816 KB
testcase_01	AC	2 ms 6,944 KB
testcase_02	AC	2 ms 6,940 KB
testcase_03	AC	2 ms 6,940 KB
testcase_04	AC	1 ms 6,944 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	2 ms 6,940 KB
testcase_07	AC	2 ms 6,944 KB
testcase_08	AC	2 ms 6,940 KB
testcase_09	AC	2 ms 6,940 KB
testcase_10	AC	2 ms 6,944 KB
testcase_11	AC	2 ms 6,944 KB
testcase_12	AC	1 ms 6,940 KB
testcase_13	AC	2 ms 6,940 KB
testcase_14	AC	6 ms 6,944 KB
testcase_15	AC	5 ms 6,944 KB
testcase_16	AC	6 ms 6,940 KB
testcase_17	AC	5 ms 6,940 KB
testcase_18	AC	5 ms 6,944 KB
testcase_19	AC	5 ms 6,940 KB
testcase_20	AC	6 ms 6,940 KB
testcase_21	AC	5 ms 6,940 KB
testcase_22	AC	6 ms 6,940 KB
testcase_23	AC	6 ms 6,940 KB
testcase_24	AC	6 ms 6,940 KB
testcase_25	AC	6 ms 6,944 KB
testcase_26	AC	6 ms 6,940 KB
testcase_27	AC	6 ms 6,940 KB
testcase_28	AC	6 ms 6,940 KB
testcase_29	AC	6 ms 6,944 KB
testcase_30	AC	6 ms 6,940 KB
testcase_31	AC	6 ms 6,944 KB
testcase_32	AC	7 ms 6,940 KB
testcase_33	AC	6 ms 6,940 KB
testcase_34	AC	2 ms 6,944 KB
testcase_35	AC	5 ms 6,944 KB
testcase_36	AC	3 ms 6,940 KB
testcase_37	AC	3 ms 6,944 KB
testcase_38	AC	2 ms 6,940 KB
testcase_39	AC	2 ms 6,944 KB
testcase_40	AC	4 ms 6,940 KB
testcase_41	AC	4 ms 6,940 KB
testcase_42	AC	4 ms 6,944 KB
testcase_43	AC	4 ms 6,940 KB
testcase_44	AC	2 ms 6,944 KB
testcase_45	AC	1 ms 6,940 KB
testcase_46	AC	2 ms 6,940 KB

権限があれば一括ダウンロードができます

コンパイルメッセージ

main.cpp:206:1: warning: ISO C++ forbids declaration of 'main' with no type [-Wreturn-type]
  206 | main()
      | ^~~~

ソースコード

raw source code

#ifdef LOCAL
    #define _GLIBCXX_DEBUG
    #define __clock__
#else
    #pragma GCC optimize("Ofast")
    // #define NDEBUG
#endif
#define __precision__ 10
#define buffer_check true
#define iostream_untie true
#define debug_stream std::cerr

#include <algorithm>
#include <bitset>
#include <cassert>
#include <chrono>
#include <complex>
#include <cstring>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <unordered_map>
#include <unordered_set>

#define all(v) std::begin(v), std::end(v)
#define rall(v) std::rbegin(v), std::rend(v)
#define odd(n) ((n) & 1)
#define even(n) (not __odd(n))
#define __popcount(n) __builtin_popcountll(n)
#define __clz32(n) __builtin_clz(n)
#define __clz64(n) __builtin_clzll(n)
#define __ctz32(n) __builtin_ctz(n)
#define __ctz64(n) __builtin_ctzll(n)

using i32 = int_least32_t; using i64 = int_least64_t; using u32 = uint_least32_t; using u64 = uint_least64_t;
using pii = std::pair<i32, i32>; using pll = std::pair<i64, i64>;
template <class T> using heap = std::priority_queue<T>;
template <class T> using rheap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <class T> using hashset = std::unordered_set<T>;
template <class Key, class Value> using hashmap = std::unordered_map<Key, Value>;

namespace execution
{
    using namespace std::chrono;
    system_clock::time_point start_time, end_time;
    long long get_elapsed_time() { end_time = system_clock::now(); return duration_cast<milliseconds>(end_time - start_time).count(); }
    void print_elapsed_time() { std::cerr << "\n----- Exec time : " << get_elapsed_time() << " ms -----\n"; }
    struct setupper
    {
        setupper()
        {
            if(iostream_untie) std::ios::sync_with_stdio(false), std::cin.tie(nullptr);
            std::cout << std::fixed << std::setprecision(__precision__);
    #ifdef stderr_path
            if(freopen(stderr_path, "a", stderr))
            {
                std::cerr << std::fixed << std::setprecision(__precision__);
            }
    #endif
    #ifdef stdout_path
            if(not freopen(stdout_path, "w", stdout))
            {
                freopen("CON", "w", stdout);
                std::cerr << "Failed to open the stdout file\n\n";
            }
            std::cout << "";
    #endif
    #ifdef stdin_path
            if(not freopen(stdin_path, "r", stdin))
            {
                freopen("CON", "r", stdin);
                std::cerr << "Failed to open the stdin file\n\n";
            }
    #endif
    #ifdef LOCAL
            std::cerr << "----- stderr at LOCAL -----\n\n";
            atexit(print_elapsed_time);
    #else
            fclose(stderr);
    #endif
    #ifdef __clock__
            start_time = system_clock::now();
    #endif
        }
    } __setupper;
    class myclock_t
    {
        system_clock::time_point built_pt, last_pt; int built_ln, last_ln;
        std::string built_func, last_func; bool is_built;
    public:
        myclock_t() : is_built(false) {}
        void build(int crt_ln, const std::string &crt_func)
        {
            is_built = true, last_pt = built_pt = system_clock::now(),  last_ln = built_ln = crt_ln, last_func = built_func = crt_func;
        }
        void set(int crt_ln, const std::string &crt_func)
        {
            if(is_built) last_pt = system_clock::now(), last_ln = crt_ln, last_func = crt_func;
            else debug_stream << "[ " << crt_ln << " : " << crt_func << " ] " << "myclock_t::set failed (yet to be built!)\n";
        }
        void get(int crt_ln, const std::string &crt_func)
        {
            if(is_built)
            {
                system_clock::time_point crt_pt(system_clock::now());
                long long diff = duration_cast<milliseconds>(crt_pt - last_pt).count();
                debug_stream << diff << " ms elapsed from" << " [ " << last_ln << " : " << last_func << " ]";
                if(last_ln == built_ln) debug_stream << " (when built)";
                debug_stream << " to" << " [ " << crt_ln << " : " << crt_func << " ]" << "\n";
                last_pt = built_pt, last_ln = built_ln, last_func = built_func;
            }
            else
            {
                debug_stream << "[ " << crt_ln << " : " << crt_func << " ] " << "myclock_t::get failed (yet to be built!)\n";
            }
        }
    };
} // namespace execution

#ifdef __clock__
    execution::myclock_t __myclock;
    #define build_clock() __myclock.build(__LINE__, __func__)
    #define set_clock() __myclock.set(__LINE__, __func__)
    #define get_clock() __myclock.get(__LINE__, __func__)
#else
    #define build_clock() ((void)0)
    #define set_clock() ((void)0)
    #define get_clock() ((void)0)
#endif

namespace std
{
    // hash
    template <class T> size_t hash_combine(size_t seed, T const &key) { return seed ^ (hash<T>()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2)); }
    template <class T, class U> struct hash<pair<T, U>> { size_t operator()(pair<T, U> const &pr) const { return hash_combine(hash_combine(0, pr.first), pr.second); } };
    template <class tuple_t, size_t index = tuple_size<tuple_t>::value - 1> struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(tuple_hash_calc<tuple_t, index - 1>::apply(seed, t), get<index>(t)); } };
    template <class tuple_t> struct tuple_hash_calc<tuple_t, 0> { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(seed, get<0>(t)); } };
    template <class... T> struct hash<tuple<T...>> { size_t operator()(tuple<T...> const &t) const { return tuple_hash_calc<tuple<T...>>::apply(0, t); } };
    // iostream
    template <class T, class U> istream &operator>>(istream &is, pair<T, U> &p) { return is >> p.first >> p.second; }
    template <class T, class U> ostream &operator<<(ostream &os, const pair<T, U> &p) { return os << p.first << ' ' << p.second; }
    template <class tuple_t, size_t index> struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { tupleos<tuple_t, index - 1>::apply(os, t); return os << ' ' << get<index>(t); } };
    template <class tuple_t> struct tupleos<tuple_t, 0> { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } };
    template <class... T> ostream &operator<<(ostream &os, const tuple<T...> &t)  { return tupleos<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(os, t); }
    template <> ostream &operator<<(ostream &os, const tuple<> &t) { return os; }
    template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> = nullptr>
    istream& operator>>(istream& is, Container &cont) { for(auto&& e : cont) is >> e; return is; }
    template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> = nullptr>
    ostream& operator<<(ostream& os, const Container &cont) { bool flag = 1; for(auto&& e : cont) flag ? flag = 0 : (os << ' ', 0), os << e; return os; }
} // namespace std

#ifdef LOCAL
    #define dump(...)                                                              \
        debug_stream << "[ " << __LINE__ << " : " << __FUNCTION__ << " ]\n",       \
            dump_func(#__VA_ARGS__, __VA_ARGS__)
    template <class T> void dump_func(const char *ptr, const T &x)
    {
        debug_stream << '\t';
        for(char c = *ptr; c != '\0'; c = *++ptr) if(c != ' ') debug_stream << c;
        debug_stream << " : " << x << '\n';
    }
    template <class T, class... rest_t> void dump_func(const char *ptr, const T &x, rest_t... rest)
    {
        debug_stream << '\t';
        for(char c = *ptr; c != ','; c = *++ptr) if(c != ' ') debug_stream << c;
        debug_stream << " : " << x << ",\n"; dump_func(++ptr, rest...);
    }
#else
    #define dump(...) ((void)0)
#endif
template <class P> void read_range(P __first, P __second) { for(P i = __first; i != __second; ++i) std::cin >> *i; }
template <class P> void write_range(P __first, P __second) { for(P i = __first; i != __second; std::cout << (++i == __second ? '\n' : ' ')) std::cout << *i; }

// substitue y for x if x > y.
template <class T> inline bool sbmin(T &x, const T &y) { return x > y ? x = y, true : false; }
// substitue y for x if x < y.
template <class T> inline bool sbmax(T &x, const T &y) { return x < y ? x = y, true : false; }
// binary search.
i64 bin(const std::function<bool(i64)> &pred, i64 ok, i64 ng)
{
    while(std::abs(ok - ng) > 1) { i64 mid = (ok + ng) / 2; (pred(mid) ? ok : ng) = mid; }
    return ok;
}
double bin(const std::function<bool(double)> &pred, double ok, double ng, const double eps)
{
    while(std::abs(ok - ng) > eps) { double mid = (ok + ng) / 2; (pred(mid) ? ok : ng) = mid; }
    return ok;
}
// be careful that val is type-sensitive.
template <class T, class A, size_t N> void init(A (&array)[N], const T &val) { std::fill((T *)array, (T *)(array + N), val); }
// reset all bits.
template <class A> void reset(A &array) { memset(array, 0, sizeof(array)); }


/* The main code follows. */

using namespace std;

main()
{
    void __solve();
    u32 t = 1;
#ifdef LOCAL
    t = 1;
#endif
    // t = -1;
    // cin >> t;
    while(t--) __solve();

    char chec;
    if(buffer_check && cin >> chec)
    {
        cerr << "\n\033[1;35mwarning\033[0m: buffer not empty.\n";
        return EXIT_FAILURE;
    }
}


template <class K>
// K must be a field.
struct matrix
{
    std::vector<std::vector<K>> mat;

    matrix() {}
    matrix(size_t n) { assign(n, n);}
    matrix(size_t h, size_t w) { assign(h, w); }
    matrix(const matrix &x) : mat(x.mat) {}
    matrix(const std::vector<std::vector<K>> _mat) : mat(_mat) {}

    void resize(size_t h, size_t w, const K v = K(0)) { mat.resize(h, std::vector<K>(w, v)); }
    void assign(size_t h, size_t w, const K v = K()) { mat.assign(h, std::vector<K>(w, v)); }

    size_t height() const { return mat.size(); }
    size_t width() const { return mat.empty() ? 0 : mat[0].size(); }
    bool is_square() const { return height() == width(); }

    std::vector<K> &operator[](const size_t i) { return mat[i]; }

    static matrix identity(size_t n)
    {
        matrix ret(n, n);
        for(size_t i = 0; i < n; ++i) ret[i][i] = K(1);
        return ret;
    }

    matrix operator-() const
    {
        size_t h = height(), w = width();
        matrix res(*this);
        for(size_t i = 0; i < h; ++i)
        {
            for(size_t j = 0; j < w; ++j)
            {
                res[i][j] = -mat[i][j];
            }
        }
        return res;
    }

    matrix operator&(const matrix &x) const { return matrix(*this) &= x; }

    matrix operator|(const matrix &x) const { return matrix(*this) |= x; }

    matrix operator^(const matrix &x) const { return matrix(*this) ^= x; }

    matrix operator+(const matrix &x) const { return matrix(*this) += x; }

    matrix operator-(const matrix &x) const { return matrix(*this) -= x; }

    matrix operator*(const matrix &x) const { return matrix(*this) *= x; }

    matrix &operator&=(const matrix &x)
    {
        size_t h = height(), w = width();
        assert(h == x.height() and w == x.width());
        for(size_t i = 0; i < h; ++i)
        {
            for(size_t j = 0; j < w; ++j)
            {
                mat[i][j] &= x.mat[i][j];
            }
        }
        return *this;
    }

    matrix &operator|=(const matrix &x)
    {
        size_t h = height(), w = width();
        assert(h == x.height() and w == x.width());
        for(size_t i = 0; i < h; ++i)
        {
            for(size_t j = 0; j < w; ++j)
            {
                mat[i][j] |= x.mat[i][j];
            }
        }
        return *this;
    }

    matrix &operator^=(const matrix &x)
    {
        size_t h = height(), w = width();
        assert(h == x.height() and w == x.width());
        for(size_t i = 0; i < h; ++i)
        {
            for(size_t j = 0; j < w; ++j)
            {
                mat[i][j] ^= x.mat[i][j];
            }
        }
        return *this;
    }

    matrix &operator+=(const matrix &x)
    {
        size_t h = height(), w = width();
        assert(h == x.height() and w == x.width());
        for(size_t i = 0; i < h; ++i)
        {
            for(size_t j = 0; j < w; ++j)
            {
                mat[i][j] += x.mat[i][j];
            }
        }
        return *this;
    }

    matrix &operator-=(const matrix &x)
    {
        size_t h = height(), w = width();
        assert(h == x.height() and w == x.width());
        for(size_t i = 0; i < h; ++i)
        {
            for(size_t j = 0; j < w; ++j)
            {
                mat[i][j] -= x.mat[i][j];
            }
        }
        return *this;
    }

    matrix &operator*=(const matrix &x)
    {
        size_t l = height(), m = width(), n = x.width();
        assert(m == x.height());
        matrix res(l, n);
        for(size_t i = 0; i < l; ++i)
        {
            for(size_t j = 0; j < m; ++j)
            {
                for(size_t k = 0; k < n; ++k)
                {
                    res[i][k] += mat[i][j] * x.mat[j][k];
                }
            }
        }
        return *this = res;
    }

    friend matrix pow(matrix x, int_fast64_t n)
    {
        assert(x.is_square());
        matrix res = identity(x.height());
        while(n)
        {
            if(n & 1) res *= x;
            x *= x, n >>= 1;
        }
        return res;
    }

    friend matrix inverse(const matrix &x)
    {
        assert(x.is_square());
        size_t n = x.height();
        matrix ext_x(x), e(identity(n)), res(n);
        for(size_t i = 0; i < n; ++i)
            ext_x[i].insert(end(ext_x[i]), begin(e[i]), end(e[i]));
        ext_x = ext_x.row_canonical_form();
        for(size_t i = 0; i < n; ++i)
        {
            if(std::vector<K>(begin(ext_x[i]), begin(ext_x[i]) + n) != e[i]) return matrix();
            res[i] = std::vector<K>(begin(ext_x[i]) + n, end(ext_x[i]));
        }
        return res;
    }

    std::vector<size_t> row_canonicalize()
    {
        std::vector<size_t> pivots;
        const size_t h = height(), w = width();
        for(size_t j = 0, rank = 0; j != w; ++j)
        {
            bool ispiv = false;
            for(size_t i = rank; i != h; ++i)
            {
                if(mat[i][j] != K{})
                {
                    if(ispiv)
                    {
                        K r = -mat[i][j];
                        for(size_t k = j; k != w; ++k) mat[i][k] += mat[rank][k] * r;
                    }
                    else
                    {
                        swap(mat[rank], mat[i]);
                        K r = mat[rank][j];
                        for(size_t k = j; k != w; ++k) mat[rank][k] /= r;
                        for(size_t k = 0; k != rank; ++k)
                        {
                            r = -mat[k][j];
                            for(size_t l = j; l != w; ++l) mat[k][l] += mat[rank][l] * r;
                        }
                        ispiv = true;
                    }
                }
            }
            if(ispiv)
            {
                ++rank;
                pivots.emplace_back(j);
            }
        }
        return pivots;
    }

    std::pair<matrix, std::vector<size_t>> row_canonical_form()
    {
        size_t h = height(), w = width(), rank = 0;
        matrix res(*this);
        std::vector<size_t> pivots;
        for(size_t j = 0; j < w; ++j)
        {
            bool piv = false;
            for(size_t i = rank; i < h; ++i)
            {
                if(res[i][j] != K(0))
                {
                    if(piv)
                    {
                        K r = -res[i][j];
                        for(size_t k = j; k < w; ++k) res[i][k] += res[rank][k] * r;
                    }
                    else
                    {
                        swap(res[rank], res[i]);
                        K r = res[rank][j];
                        for(size_t k = j; k < w; ++k) res[rank][k] /= r;
                        for(size_t k = 0; k < rank; ++k)
                        {
                            r = -res[k][j];
                            for(size_t l = j; l < w; ++l) res[k][l] += res[rank][l] * r;
                        }
                        piv = true;
                        pivots.emplace_back(j);
                    }
                }
            }
            if(piv) ++rank;
        }
        return {res, pivots};
    }

    K determinant() const
    {
        matrix<K> x(*this);
        assert(is_square());
        size_t n = height();
        K res(1);
        for(size_t j = 0; j < n; ++j)
        {
            bool piv = false;
            for(size_t i = j; i < n; ++i)
            {
                if(x[i][j] != K(0))
                {
                    if(piv)
                    {
                        const K r = -x[i][j];
                        for(size_t k = j; k < n; ++k) x[i][k] += x[j][k] * r;
                    }
                    else
                    {
                        swap(x[i], x[j]);
                        if(i != j) res = -res;
                        const K r = x[j][j];
                        res *= r;
                        for(size_t k = j; k < n; ++k) x[j][k] /= r;
                        piv = true;
                    }
                }
            }
            if(not piv) return K(0);
        }
        return res;
    }

    friend std::istream &operator>>(std::istream &s, matrix &x)
    {
        size_t h = x.height(), w = x.width();
        for(size_t i = 0; i < h; ++i)
        {
            for(size_t j = 0; j < w; ++j) s >> x[i][j];
        }
        return s;
    }

    friend std::ostream &operator<<(std::ostream &s, const matrix &x)
    {
        size_t h = x.height(), w = x.width();
        for(size_t i = 0; i < h; ++i)
        {
            if(i) s << "\n";
            for(size_t j = 0; j < w; ++j) s << (j ? " " : "") << x.mat[i][j];
        }
        return s;
    }
};

#ifndef MODULO_HPP
#define MODULO_HPP

#include <bits/stdc++.h>

namespace math
{
    template <int mod>
    class modint
    {
        int val;
      public:
        constexpr modint() : val{0} {}
        constexpr modint(long long x) : val((x %= mod) < 0 ? mod + x : x) {}
        constexpr long long get() const { return val; }
        constexpr modint &operator+=(const modint &other) { return (val += other.val) < mod ? 0 : val -= mod, *this; }
        constexpr modint &operator++() { return ++val, *this; }
        constexpr modint operator++(int) { modint t = *this; return ++val, t; }
        constexpr modint &operator-=(const modint &other) { return (val += mod - other.val) < mod ? 0 : val -= mod, *this; }
        constexpr modint &operator--() { return --val, *this; }
        constexpr modint operator--(int) { modint t = *this; return --val, t; }
        constexpr modint &operator*=(const modint &other) { return val = (long long)val * other.val % mod, *this; }
        constexpr modint &operator/=(const modint &other) { return *this *= inverse(other); }
        constexpr modint operator-() const { return modint(-val); }
        constexpr modint operator+(const modint &other) const { return modint(*this) += other; }
        constexpr modint operator-(const modint &other) const { return modint(*this) -= other; }
        constexpr modint operator*(const modint &other) const { return modint(*this) *= other; }
        constexpr modint operator/(const modint &other) const { return modint(*this) /= other; }
        constexpr bool operator==(const modint &other) const { return val == other.val; }
        constexpr bool operator!=(const modint &other) const { return val != other.val; }
        constexpr bool operator!() const { return !val; }
        friend constexpr modint inverse(const modint &other)
        {
            assert(other != 0);
            int a{mod}, b{other.val}, u{}, v{1}, t{};
            while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v;
            return modint{u};
        }
        friend constexpr modint pow(modint other, long long e)
        {
            if(e < 0) e = e % (mod - 1) + mod - 1;
            modint res{1};
            while(e) { if(e & 1) res *= other; other *= other, e >>= 1; }
            return res;
        }
        friend std::ostream &operator<<(std::ostream &s, const modint &other) { return s << other.val; }
        friend std::istream &operator>>(std::istream &s, modint &other) { long long val; other = modint{(s >> val, val)}; return s; }
    }; // class modint
} // namespace math

namespace math
{
    template <>
    class modint<2>
    {
        bool val;
      public:
        constexpr modint(bool x = false) : val{x} {}
        constexpr modint(int x) : val(x & 1) {}
        constexpr modint(long long x) : val(x & 1) {}
        constexpr bool get() const { return val; }
        constexpr modint &operator+=(const modint &other) { return val ^= other.val, *this; }
        constexpr modint &operator++() { return val = !val, *this; }
        constexpr modint operator++(int) { modint t = *this; return val = !val, t; }
        constexpr modint &operator-=(const modint &other) { return val ^= other.val, *this; }
        constexpr modint &operator--() { return val = !val, *this; }
        constexpr modint operator--(int) { modint t = *this; return val = !val, t; }
        constexpr modint &operator*=(const modint &other) { return val &= other.val, *this; }
        constexpr modint &operator/=(const modint &other) { return *this; }
        constexpr modint operator-() const { return *this; }
        constexpr modint operator+(const modint &other) const { return val != other.val; }
        constexpr modint operator-(const modint &other) const { return val != other.val; }
        constexpr modint operator*(const modint &other) const { return val && other.val; }
        constexpr modint operator/(const modint &other) const { return *this; }
        constexpr bool operator==(const modint &other) const { return val == other.val; }
        constexpr bool operator!=(const modint &other) const { return val != other.val; }
        constexpr bool operator!() const { return !val; }
        operator bool() const { return val; }
        friend constexpr modint inverse(const modint &other) { return other; }
        friend constexpr modint pow(const modint &other, long long exp) { return other; }
        friend std::ostream &operator<<(std::ostream &os, const modint &other) { return os << other.val; }
        friend std::istream &operator>>(std::istream &is, modint &other) { long long val; other.val = (is >> val, val & 1); return is; }
    };
}

#endif

using namespace math;


void __solve()
{
    int n,m,X; cin>>n>>m>>X;
    matrix<modint<2>> mat(30+m,n+1);
    for(int i=0; i<n; ++i)
    {
        int x; cin>>x;
        for(int k=0; k<30; ++k)
        {
            mat[k][i]=x;
            x>>=1;
        }
    }
    for(int k=0; k<30; ++k)
    {
        mat[k][n]=X;
        X>>=1;
    }
    for(int i=30; i<m+30; ++i)
    {
        int typ,l,r; cin>>typ>>l>>r;
        mat[i][n]=typ;
        for(int j=l-1; j<r; ++j)
        {
            mat[i][j]=1;
        }
    }

    vector<size_t> pv(mat.row_canonicalize());
    if(!pv.empty()&&pv.back()==n)
    {
        cout << 0 << "\n";
    }
    else
    {
        cout << pow(modint<1000000007>(2),n-pv.size()) << "\n";
    }
}

yukicoder

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