#708010 (C++17) No.803 Very Limited Xor Subset

• 問題: No.803 Very Limited Xor Subset
• ユーザー: rniya
• 提出日時: 2021-10-17 17:10:52
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 3 ms / 2,000 ms
• コード長: 11,402 bytes
• コンパイル時間: 2,297 ms
• コンパイル使用メモリ: 201,344 KB
• 最終ジャッジ日時: 2025-01-25 01:44:47
• ジャッジサーバーID （参考情報）: judge1 / judge2

ファイルパターン	結果
sample	AC * 4
other	AC * 43

ソースコード

#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()

template <typename T> istream& operator>>(istream& is, vector<T>& v) {
    for (T& x : v) is >> x;
    return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
    for (int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
    }
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << '(' << p.first << ',' << p.second << ')';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
    for (int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
    }
    return os;
}

template <int i, typename T> void print_tuple(ostream&, const T&) {}
template <int i, typename T, typename H, class... Args> void print_tuple(ostream& os, const T& t) {
    if (i) os << ',';
    os << get<i>(t);
    print_tuple<i + 1, T, Args...>(os, t);
}
template <typename... Args> ostream& operator<<(ostream& os, const tuple<Args...>& t) {
    os << '{';
    print_tuple<0, tuple<Args...>, Args...>(os, t);
    return os << '}';
}

void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
    cerr << head;
    if (sizeof...(Tail) > 0) cerr << ", ";
    debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...)                                                                   \
    cerr << " ";                                                                     \
    cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
    cerr << " ";                                                                     \
    debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }

int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(long long t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }

template <class T> T ceil(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <class T> T floor(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? x / y : (x - y + 1) / y);
}

template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
#pragma endregion

#include <cassert>
#include <cstdint>
#include <iostream>

template <uint64_t Modulus> class modint {
    using i64 = int64_t;
    using u32 = uint32_t;
    using u64 = uint64_t;

    static_assert(Modulus < static_cast<uint32_t>(1) << 31, "Modulus must be less than 2**31");
    static constexpr u32 mod = Modulus;
    u32 v;

public:
    constexpr modint(const i64 x = 0) noexcept : v(x < 0 ? mod - 1 - (-(x + 1) % mod) : x % mod) {}
    constexpr u32& val() noexcept { return v; }
    constexpr const u32& val() const noexcept { return v; }
    constexpr modint operator+(const modint& rhs) const noexcept { return modint(*this) += rhs; }
    constexpr modint operator-(const modint& rhs) const noexcept { return modint(*this) -= rhs; }
    constexpr modint operator*(const modint& rhs) const noexcept { return modint(*this) *= rhs; }
    constexpr modint operator/(const modint& rhs) const noexcept { return modint(*this) /= rhs; }
    constexpr modint& operator+=(const modint& rhs) noexcept {
        v += rhs.v;
        if (v >= mod) v -= mod;
        return *this;
    }
    constexpr modint& operator-=(const modint& rhs) noexcept {
        if (v < rhs.v) v += mod;
        v -= rhs.v;
        return *this;
    }
    constexpr modint& operator*=(const modint& rhs) noexcept {
        v = (u64)v * rhs.v % mod;
        return *this;
    }
    constexpr modint& operator/=(const modint& rhs) noexcept { return *this *= rhs.inv(); }
    constexpr modint pow(long long n) const noexcept {
        assert(0 <= n);
        modint self(*this), res(1);
        while (n > 0) {
            if (n & 1) res *= self;
            self *= self;
            n >>= 1;
        }
        return res;
    }
    constexpr modint inv() const noexcept {
        assert(*this != 0);
        return pow(mod - 2);
    }
    constexpr modint& operator++() noexcept {
        if (++v == mod) v = 0;
        return *this;
    }
    constexpr modint& operator--() noexcept {
        if (v == 0) v = mod;
        return --v, *this;
    }
    constexpr modint operator++(int) noexcept {
        modint t = *this;
        return ++*this, t;
    }
    constexpr modint operator--(int) noexcept {
        modint t = *this;
        return --*this, t;
    }
    constexpr modint operator-() const noexcept { return modint(mod - v); }
    template <class T> friend constexpr modint operator+(T x, modint y) noexcept { return modint(x) + y; }
    template <class T> friend constexpr modint operator-(T x, modint y) noexcept { return modint(x) - y; }
    template <class T> friend constexpr modint operator*(T x, modint y) noexcept { return modint(x) * y; }
    template <class T> friend constexpr modint operator/(T x, modint y) noexcept { return modint(x) / y; }
    constexpr bool operator==(const modint& rhs) const noexcept { return v == rhs.v; }
    constexpr bool operator!=(const modint& rhs) const noexcept { return v != rhs.v; }
    constexpr bool operator!() const noexcept { return !v; }
    friend std::istream& operator>>(std::istream& s, modint& rhs) noexcept {
        i64 v;
        rhs = modint{(s >> v, v)};
        return s;
    }
    friend std::ostream& operator<<(std::ostream& s, const modint& rhs) noexcept { return s << rhs.v; }
};

/**
 * @brief modint
 * @docs docs/modulo/modint.md
 */

#include <bitset>
#include <cassert>
#include <vector>

template <size_t MAX_COL> struct BitMatrix {
    size_t n, m;
    std::vector<std::bitset<MAX_COL>> A;

    BitMatrix(size_t n, size_t m) : n(n), m(m), A(n) { assert(m <= MAX_COL); }

    size_t size() const { return n; };

    size_t height() const { return n; }

    size_t width() const { return m; }

    inline const std::bitset<MAX_COL>& operator[](int k) const { return A[k]; }

    inline std::bitset<MAX_COL>& operator[](int k) { return A[k]; }

    static BitMatrix I(size_t n) {
        BitMatrix res(n, n);
        for (size_t i = 0; i < n; i++) res[i][i] = true;
        return res;
    }

    BitMatrix& operator*=(const BitMatrix& B) {
        assert(m == B.height());
        BitMatrix C(n, B.width());
        for (size_t i = 0; i < n; i++) {
            for (size_t j = 0; j < m; j++) {
                if (A[i][j]) {
                    C[i] |= B[j];
                }
            }
        }
        std::swap(A, C.A);
        return *this;
    }

    BitMatrix& operator^=(long long k) {
        assert(0 <= k);
        BitMatrix B = BitMatrix::I(n);
        while (k > 0) {
            if (k & 1) B *= *this;
            *this *= *this;
            k >>= 1;
        }
        std::swap(A, B.A);
        return *this;
    }

    BitMatrix operator*(const BitMatrix& B) const { return BitMatrix(*this) *= B; }

    BitMatrix operator^(const long long k) const { return BitMatrix(*this) ^= k; }

    size_t gauss_jordan() {
        size_t rank = 0;
        for (size_t j = 0; j < m; j++) {
            int pivot = -1;
            for (size_t i = rank; i < n; i++) {
                if (A[i][j]) {
                    pivot = i;
                    break;
                }
            }
            if (pivot == -1) continue;
            std::swap(A[pivot], A[rank]);
            for (size_t i = 0; i < n; i++) {
                if (i != rank and A[i][j]) {
                    A[i] ^= A[rank];
                }
            }
            rank++;
        }
        return rank;
    }

    std::pair<int, std::bitset<MAX_COL>> system_of_linear_equations(const std::vector<bool>& b) {
        assert(m + 1 <= MAX_COL);
        BitMatrix B(*this);
        for (size_t i = 0; i < n; i++) B[i][m] = b[i];
        size_t rank = B.gauss_jordan();
        for (size_t i = rank; i < n; i++) {
            if (B[i][m]) {
                return {-1, std::bitset<MAX_COL>()};
            }
        }
        std::bitset<MAX_COL> res;
        for (size_t i = 0; i < rank; i++) res[i] = A[i][m];
        return {rank, res};
    }
};

const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
const long long MOD = 1000000007;
// const long long MOD = 998244353;

const int MAX_LOG = 30, MAX_N = 305, MAX = MAX_LOG + MAX_N;
using BM = BitMatrix<MAX_N>;
using mint = modint<1000000007>;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N, M, X;
    cin >> N >> M >> X;
    BM A(MAX_LOG + MAX_N, N);
    vector<bool> b(MAX_LOG + MAX_N);
    for (int i = 0; i < MAX_LOG; i++, X >>= 1) b[i] = X & 1;
    for (int i = 0; i < N; i++) {
        int a;
        cin >> a;
        for (int j = 0; j < MAX_LOG; j++, a >>= 1) A[j][i] = a & 1;
    }
    for (int i = 0; i < M; i++) {
        int t, l, r;
        cin >> t >> l >> r;
        for (int j = --l; j < r; j++) A[MAX_LOG + i][j] = 1;
        b[MAX_LOG + i] = t;
    }

    int rank = A.system_of_linear_equations(b).first;
    if (rank == -1) {
        cout << 0 << '\n';
        return 0;
    }
    mint ans = mint(2).pow(N - rank);
    cout << ans << '\n';
    return 0;
}