#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; }