This documentation is automatically generated by online-judge-tools/verification-helper
This project is maintained by tsutaj
#include <vector>
#include <algorithm>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <iomanip>
using namespace std;
#include "../math_017_modint.cpp"
#include "../math_004_matrix.cpp"
#include "../math_023_matrix_utils_modp.cpp"
void ARC054_C() {
using mint = ModInt<2>;
int N; cin >> N;
Matrix<mint> mat(N, N);
for(int i=0; i<N; i++) {
for(int j=0; j<N; j++) {
char c; cin >> c;
if(c == '1') mat[i][j] = mint(1);
}
}
mint d = detModp(mat);
if(d == mint(0)) cout << "Even" << endl;
else cout << "Odd" << endl;
}
void yuki_803() {
using mint = ModInt<2>;
const int B = 30;
int N, M, X; cin >> N >> M >> X;
Matrix<mint> mat(B+M, N+1);
for(int j=0; j<B; j++) {
int p = X & 1;
mat[j][N] = mint(p);
X >>= 1;
}
for(int i=0; i<N; i++) {
int val; cin >> val;
for(int j=0; j<B; j++) {
int p = val & 1;
mat[j][i] = mint(p);
val >>= 1;
}
}
for(int i=0; i<M; i++) {
int t, l, r; cin >> t >> l >> r; l--;
mat[B+i][N] = t;
for(int x=l; x<r; x++) mat[B+i][x] = 1;
}
int rank = gaussianEliminationModp(mat, true);
for(int i=rank; i<B+M; i++) {
if(mat[i][N] != mint(0)) {
cout << 0 << endl;
return;
}
}
int p = N - rank;
cout << ModInt<1000000007>(2).pow(p) << endl;
}
int main() {
// ARC054_C(); // detModp
yuki_803(); // gaussianEliminationModp
}
#line 1 "math/verify/verify_math_023_matrix_utils_modp.cpp"
#include <vector>
#include <algorithm>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <iomanip>
using namespace std;
#line 1 "math/math_017_modint.cpp"
// ModInt begin
using ll = long long;
template<ll mod>
struct ModInt {
ll v;
ll mod_pow(ll x, ll n) const {
return (!n) ? 1 : (mod_pow((x*x)%mod,n/2) * ((n&1)?x:1)) % mod;
}
ModInt(ll a = 0) : v((a %= mod) < 0 ? a + mod : a) {}
ModInt operator+ ( const ModInt& b ) const {
return (v + b.v >= mod ? ModInt(v + b.v - mod) : ModInt(v + b.v));
}
ModInt operator- () const {
return ModInt(-v);
}
ModInt operator- ( const ModInt& b ) const {
return (v - b.v < 0 ? ModInt(v - b.v + mod) : ModInt(v - b.v));
}
ModInt operator* ( const ModInt& b ) const {return (v * b.v) % mod;}
ModInt operator/ ( const ModInt& b ) const {return (v * mod_pow(b.v, mod-2)) % mod;}
bool operator== ( const ModInt &b ) const {return v == b.v;}
bool operator!= ( const ModInt &b ) const {return !(*this == b); }
ModInt& operator+= ( const ModInt &b ) {
v += b.v;
if(v >= mod) v -= mod;
return *this;
}
ModInt& operator-= ( const ModInt &b ) {
v -= b.v;
if(v < 0) v += mod;
return *this;
}
ModInt& operator*= ( const ModInt &b ) {
(v *= b.v) %= mod;
return *this;
}
ModInt& operator/= ( const ModInt &b ) {
(v *= mod_pow(b.v, mod-2)) %= mod;
return *this;
}
ModInt pow(ll x) { return ModInt(mod_pow(v, x)); }
// operator int() const { return int(v); }
// operator long long int() const { return v; }
};
template<ll mod>
ModInt<mod> pow(ModInt<mod> n, ll k) {
return ModInt<mod>(n.mod_pow(n.v, k));
}
template<ll mod>
ostream& operator<< (ostream& out, ModInt<mod> a) {return out << a.v;}
template<ll mod>
istream& operator>> (istream& in, ModInt<mod>& a) {
in >> a.v;
return in;
}
// ModInt end
#line 1 "math/math_004_matrix.cpp"
// 行列ライブラリ
// size(): 行数を返す (列数は mat[0].size() で)
// 演算子: 複合代入 (+=, *=, -=), 単項 (-), 二項 (+, -, *, ==)
// eigen(N): N*N 単位行列を返す
// pow(mat, k): mat の k 乗を返す
template <typename T>
struct Matrix {
vector< vector<T> > mat;
Matrix() {}
Matrix(int h, int w, T val = T(0)) : mat(h, vector<T>(w, val)) {}
size_t size() const { return mat.size(); }
const vector<T>& operator[](int i) const { return mat[i]; }
vector<T>& operator[](int i) { return mat[i]; }
Matrix<T> &operator+=(const Matrix<T>& rhs) {
assert(mat.size() == rhs.size());
assert(mat[0].size() == rhs[0].size());
for(size_t i=0; i<mat.size(); i++) {
for(size_t j=0; j<mat[0].size(); j++) {
mat[i][j] += rhs[i][j];
}
}
return *this;
}
Matrix<T> operator-() const {
Matrix<T> res(*this);
for(size_t i=0; i<res.size(); i++) {
for(size_t j=0; j<res[0].size(); j++) {
res[i][j] *= T(-1);
}
}
return res;
}
Matrix<T>& operator-=(const Matrix<T>& rhs) {
return (Matrix<T>(*this) += -rhs);
}
Matrix<T>& operator*=(const Matrix<T>& rhs) {
assert(mat[0].size() == rhs.size());
size_t H = mat.size(), W = rhs[0].size(), C = rhs.size();
Matrix<T> res(H, W);
for(size_t i=0; i<H; i++) {
for(size_t j=0; j<W; j++) {
for(size_t k=0; k<C; k++) {
res[i][j] += mat[i][k] * rhs[k][j];
}
}
}
this->mat = res.mat;
return *this;
}
Matrix<T> operator+(const Matrix<T>& rhs) {
return (Matrix<T>(*this) += rhs);
}
Matrix<T> operator*(const Matrix<T>& rhs) {
return (Matrix<T>(*this) *= rhs);
}
Matrix<T> operator-(const Matrix<T> &rhs) {
return (Matrix<T>(*this) -= rhs);
}
bool operator==(const Matrix<T> &rhs) const {
return this->mat == rhs.mat;
}
bool operator!=(const Matrix<T> &rhs) const {
return !(*this == rhs);
}
};
template <typename T>
Matrix<T> eigen(size_t N) {
Matrix<T> res(N, N, 0);
for(size_t i=0; i<N; i++) res[i][i] = T(1);
return res;
}
template <typename T>
Matrix<T> pow(Matrix<T> mat, long long int k) {
Matrix<T> res = eigen<T>(mat.size());
for(; k>0; k>>=1) {
if(k & 1) res *= mat;
mat *= mat;
}
return res;
}
template <typename T>
ostream& operator<< (ostream& out, Matrix<T> mat) {
int H = mat.size(), W = mat[0].size();
out << "[" << endl;
for(int i=0; i<H; i++) {
out << " [ ";
for(int j=0; j<W; j++) out << mat[i][j] << " ";
out << "]" << endl;
}
out << "]" << endl;
return out;
}
#line 1 "math/math_023_matrix_utils_modp.cpp"
// mod p 行列に対する主要な操作
// 実数じゃないので絶対値最大のものを pivot にするとかがいらない
// ガウスの消去法
template <typename mint>
int gaussianEliminationModp(Matrix<mint> &mat, bool ext=false) {
int N = mat.size(), M = mat[0].size(), rank = 0;
for(int j=0; j+ext<M; j++) {
int piv = -1;
for(int i=rank; i<N; i++) {
if(mat[i][j] != mint(0)) piv = i, i = N;
}
if(piv < 0) continue;
swap(mat[rank], mat[piv]);
mint div(mat[rank][j]);
for(auto &v : mat[rank]) v /= div;
for(int i=0; i<N; i++) {
if(i == rank or mat[i][j] == mint(0)) continue;
mint scale = mat[i][j];
for(int k=0; k<M; k++) {
mat[i][k] -= mat[rank][k] * scale;
}
}
rank++;
}
return rank;
}
template <typename mint>
vector<mint> linearEquationModp(Matrix<mint> A, vector<mint> b) {
int N = A.size(), M = A[0].size();
Matrix<mint> mat(N, M+1);
for(int i=0; i<N; i++) {
for(int j=0; j<M+1; j++) {
mat[i][j] = (j < M ? A[i][j] : b[i]);
}
}
int rank = gaussianEliminationModp(mat, true);
vector<mint> res(N);
for(int i=0; i<N; i++) {
res[i] = mat[i][M];
if(i >= rank and mat[i][M] != mint(0)) return {};
}
return res;
}
template <typename mint>
mint detModp(Matrix<mint> A) {
int N = A.size(), cnt_swap = 0;
for(int j=0; j<N; j++) {
int piv = -1;
for(int i=j; i<N; i++) {
if(A[i][j] != mint(0)) piv = i, i = N;
}
if(piv < 0) return mint(0);
cnt_swap += (piv != j);
swap(A[piv], A[j]);
for(int i=j+1; i<N; i++) {
mint scale(A[i][j] / A[j][j]);
for(int k=0; k<N; k++) {
A[i][k] -= A[j][k] * scale;
}
}
}
mint res = (cnt_swap % 2 ? mint(-1) : mint(1));
for(int i=0; i<N; i++) res *= A[i][i];
return res;
}
#line 11 "math/verify/verify_math_023_matrix_utils_modp.cpp"
void ARC054_C() {
using mint = ModInt<2>;
int N; cin >> N;
Matrix<mint> mat(N, N);
for(int i=0; i<N; i++) {
for(int j=0; j<N; j++) {
char c; cin >> c;
if(c == '1') mat[i][j] = mint(1);
}
}
mint d = detModp(mat);
if(d == mint(0)) cout << "Even" << endl;
else cout << "Odd" << endl;
}
void yuki_803() {
using mint = ModInt<2>;
const int B = 30;
int N, M, X; cin >> N >> M >> X;
Matrix<mint> mat(B+M, N+1);
for(int j=0; j<B; j++) {
int p = X & 1;
mat[j][N] = mint(p);
X >>= 1;
}
for(int i=0; i<N; i++) {
int val; cin >> val;
for(int j=0; j<B; j++) {
int p = val & 1;
mat[j][i] = mint(p);
val >>= 1;
}
}
for(int i=0; i<M; i++) {
int t, l, r; cin >> t >> l >> r; l--;
mat[B+i][N] = t;
for(int x=l; x<r; x++) mat[B+i][x] = 1;
}
int rank = gaussianEliminationModp(mat, true);
for(int i=rank; i<B+M; i++) {
if(mat[i][N] != mint(0)) {
cout << 0 << endl;
return;
}
}
int p = N - rank;
cout << ModInt<1000000007>(2).pow(p) << endl;
}
int main() {
// ARC054_C(); // detModp
yuki_803(); // gaussianEliminationModp
}