noya2_Library
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test/data_structure/Unionfind_with_Potential_NonCommutative_Group.test.cpp
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- Last update: 2024-08-13 15:46:43+09:00
- Problem: https://judge.yosupo.jp/problem/unionfind_with_potential_non_commutative_group
Depends on
- data_structure/potentialized_dsu.hpp
- math/matrix.hpp
- math/prime.hpp
- misc/concepts.hpp
- template/const.hpp
- template/inout_old.hpp
- template/template.hpp
- template/utils.hpp
- utility/modint.hpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/unionfind_with_potential_non_commutative_group"
#include"../../template/template.hpp"
#include"data_structure/potentialized_dsu.hpp"
#include"math/matrix.hpp"
#include"utility/modint.hpp"
using mint = modint998244353;
using mat = matrix<mint,2>;
struct G {
using value_type = mat;
static mat op(mat a, mat b){
return a * b;
}
static mat e(){
return mat::e();
}
static mat inv(mat a){
return mat(array<mint,4uz>{a[1][1],-a[0][1],-a[1][0],a[0][0]});
}
};
int main(){
int n, q; in(n,q);
potentialized_dsu<G> d(n);
while (q--){
int t; in(t);
if (t == 0){
int u, v; in(u,v);
mat x; in(x);
int l = d.merge(u,v,x);
out(l == -1 ? 0 : 1);
}
if (t == 1){
int u, v; in(u,v);
if (d.same(u,v)){
mat x = d.diff(u,v);
out(x[0][0],x[0][1],x[1][0],x[1][1]);
}
else {
out(-1);
}
}
}
}#line 1 "test/data_structure/Unionfind_with_Potential_NonCommutative_Group.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/unionfind_with_potential_non_commutative_group"
#line 2 "template/template.hpp"
using namespace std;
#include<bits/stdc++.h>
#line 1 "template/inout_old.hpp"
namespace noya2 {
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>
istream &operator>>(istream &is, pair<T, U> &p){
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
for (auto &x : v) is >> x;
return is;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
template<typename T>
void out(const vector<vector<T>> &vv){
int s = (int)vv.size();
for (int i = 0; i < s; i++) out(vv[i]);
}
struct IoSetup {
IoSetup(){
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetup_noya2;
} // namespace noya2
#line 1 "template/const.hpp"
namespace noya2{
const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 = 998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";
void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }
} // namespace noya2
#line 2 "template/utils.hpp"
#line 6 "template/utils.hpp"
namespace noya2{
unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
if (a == 0 || b == 0) return a + b;
int n = __builtin_ctzll(a); a >>= n;
int m = __builtin_ctzll(b); b >>= m;
while (a != b) {
int mm = __builtin_ctzll(a - b);
bool f = a > b;
unsigned long long c = f ? a : b;
b = f ? b : a;
a = (c - b) >> mm;
}
return a << std::min(n, m);
}
template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }
long long sqrt_fast(long long n) {
if (n <= 0) return 0;
long long x = sqrt(n);
while ((x + 1) * (x + 1) <= n) x++;
while (x * x > n) x--;
return x;
}
template<typename T> T floor_div(const T n, const T d) {
assert(d != 0);
return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}
template<typename T> T ceil_div(const T n, const T d) {
assert(d != 0);
return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}
template<typename T> void uniq(std::vector<T> &v){
std::sort(v.begin(),v.end());
v.erase(unique(v.begin(),v.end()),v.end());
}
template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }
template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }
template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }
} // namespace noya2
#line 8 "template/template.hpp"
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;
namespace noya2{
/* ~ (. _________ . /) */
}
using namespace noya2;
#line 4 "test/data_structure/Unionfind_with_Potential_NonCommutative_Group.test.cpp"
#line 2 "data_structure/potentialized_dsu.hpp"
#line 6 "data_structure/potentialized_dsu.hpp"
#line 2 "misc/concepts.hpp"
#include<concepts>
namespace noya2 {
template<class monoid>
concept Monoid = requires {
typename monoid::value_type;
{monoid::op(declval<typename monoid::value_type>(),declval<typename monoid::value_type>())} -> std::same_as<typename monoid::value_type>;
{monoid::e()} -> std::same_as<typename monoid::value_type>;
};
template<class group>
concept Group = requires {
requires Monoid<group>;
{group::inv(declval<typename group::value_type>())} -> std::same_as<typename group::value_type>;
};
} // namespace noya2
#line 8 "data_structure/potentialized_dsu.hpp"
namespace noya2 {
template<Group G>
struct potentialized_dsu {
using T = typename G::value_type;
potentialized_dsu (int n = 0) : _n(n), parent_or_size(n,-1), pot(n, G::e()) {}
// p[u] = op(p[v], d), u is higher than v by d
int merge(int u, int v, T d){
int x = leader(u), y = leader(v);
if (x == y){
if (diff(u, v) == d) return x;
else return -1;
}
d = G::op(potential(u), G::inv(G::op(potential(v), d)));
if (-parent_or_size[x] < -parent_or_size[y]){
d = G::inv(d);
std::swap(x, y);
}
parent_or_size[x] += parent_or_size[y];
parent_or_size[y] = x;
pot[y] = d;
return x;
}
int leader(int v){
assert(0 <= v && v < _n);
if (parent_or_size[v] < 0) return v;
int l = leader(parent_or_size[v]);
pot[v] = G::op(pot[parent_or_size[v]], pot[v]);
return parent_or_size[v] = l;
}
bool same(int u, int v){
return leader(u) == leader(v);
}
int size(int v){
return -parent_or_size[leader(v)];
}
T potential(int v){
leader(v);
return pot[v];
}
// p[u] = op(p[v], d)
// d = op(inv(p[v]), p[u])
T diff(int u, int v){
return G::op(G::inv(potential(v)), potential(u));
}
std::vector<std::vector<int>> groups() {
std::vector<int> leader_buf(_n), group_size(_n);
for (int i = 0; i < _n; i++) {
leader_buf[i] = leader(i);
group_size[leader_buf[i]]++;
}
std::vector<std::vector<int>> result(_n);
for (int i = 0; i < _n; i++) {
result[i].reserve(group_size[i]);
}
for (int i = 0; i < _n; i++) {
result[leader_buf[i]].push_back(i);
}
result.erase(
std::remove_if(result.begin(), result.end(),
[&](const std::vector<int>& v) { return v.empty(); }),
result.end());
return result;
}
private:
int _n;
std::vector<int> parent_or_size;
std::vector<T> pot;
};
} // namespace noya2
#line 2 "math/matrix.hpp"
#line 6 "math/matrix.hpp"
#include <ranges>
#line 8 "math/matrix.hpp"
namespace noya2 {
template<typename T, size_t hw = -1uz>
struct matrix {
static constexpr int h = hw, w = hw;
std::array<T, hw*hw> m;
matrix () : m({}) {}
matrix (const std::array<T, hw*hw> &_m) : m(_m) {}
matrix (const std::array<std::array<T, hw>, hw> &_m){
for (int i = 0; i < h; i++) for (int j = 0; j < w; j++){
m[idx(i,j)] = _m[i][j];
}
}
matrix (const std::vector<std::vector<T>> &_m){
for (int i = 0; i < h; i++) for (int j = 0; j < w; j++){
m[idx(i,j)] = _m[i][j];
}
}
auto operator[](int i) const {
return std::ranges::subrange(m.begin()+i*w,m.begin()+(i+1)*w);
}
auto operator[](int i){
return std::ranges::subrange(m.begin()+i*w,m.begin()+(i+1)*w);
}
matrix &operator+= (const matrix &r){
for (int i = 0; i < h; ++i){
for (int j = 0; j < w; ++j){
m[idx(i,j)] += r.m[idx(i,j)];
}
}
return *this;
}
matrix &operator-= (const matrix &r){
for (int i = 0; i < h; ++i){
for (int j = 0; j < w; ++j){
m[idx(i,j)] -= r.m[idx(i,j)];
}
}
return *this;
}
matrix &operator*= (const matrix &r){
matrix ret;
for (int i = 0; i < h; i++){
for (int k = 0; k < w; k++){
for (int j = 0; j < r.w; j++){
ret.m[idx(i,j)] += m[idx(i,k)] * r.m[idx(k,j)];
}
}
}
return *this = ret;
}
matrix operator+ (const matrix &r) const { return matrix(*this) += r; }
matrix operator- (const matrix &r) const { return matrix(*this) -= r; }
matrix operator* (const matrix &r) const { return matrix(*this) *= r; }
matrix& operator*=(const T &r){
for (int i = 0; i < h; ++i){
for (int j = 0; j < w; ++j){
m[idx(i,j)] *= r;
}
}
return *this;
}
friend matrix operator* (const T &r, const matrix &mat){
return matrix(mat) *= r;
}
friend matrix operator* (const matrix &mat, const T &r){
return matrix(mat) *= r;
}
matrix pow(long long n){
if (n == 0) return e();
matrix f = pow(n / 2);
matrix ret = f * f;
if (n & 1) ret *= (*this);
return ret;
}
int idx(int i, int j){
return i * w + j;
}
static matrix e(){
matrix ret;
for (int i = 0; i < h; i++){
ret[i][i] = T(1);
}
return ret;
}
friend std::ostream &operator<<(std::ostream &os, const matrix &mat){
for (int i = 0; i < mat.h; i++){
if (i != 0) os << '\n';
for (int j = 0; j < mat.w; j++){
if (j != 0) os << ' ';
os << mat[i][j];
}
}
return os;
}
friend std::istream &operator>>(std::istream &is, matrix &mat){
for (int i = 0; i < mat.h; i++){
for (int j = 0; j < mat.w; j++){
is >> mat[i][j];
}
}
return is;
}
friend bool operator==(const matrix &a, const matrix &b){
for (int i = 0; i < a.h; i++){
for (int j = 0; j < a.w; j++){
if (a[i][j] != b[i][j]){
return false;
}
}
}
return true;
}
};
template<typename T>
struct matrix<T,-1uz> {
int h, w;
std::vector<T> m;
matrix () {}
matrix (int _h) : matrix(_h,_h) {}
matrix (int _h, int _w) : h(_h), w(_w), m(_h*_w) {}
matrix (int _h, int _w, const std::vector<T> &_m) : h(_h), w(_w), m(_m) {
assert((int)_m.size() == _h*_w);
}
matrix (const std::vector<std::vector<T>> &_m){
h = _m.size();
assert(h >= 1);
w = _m[0].size();
for (int i = 0; i < h; i++) for (int j = 0; j < w; j++){
m[idx(i,j)] = _m[i][j];
}
}
auto operator[](int i) const {
return std::ranges::subrange(m.begin()+i*w,m.begin()+(i+1)*w);
}
auto operator[](int i){
return std::ranges::subrange(m.begin()+i*w,m.begin()+(i+1)*w);
}
matrix &operator+= (const matrix &r){
for (int i = 0; i < h; ++i){
for (int j = 0; j < w; ++j){
m[idx(i,j)] += r.m[idx(i,j)];
}
}
return *this;
}
matrix &operator-= (const matrix &r){
for (int i = 0; i < h; ++i){
for (int j = 0; j < w; ++j){
m[idx(i,j)] -= r.m[idx(i,j)];
}
}
return *this;
}
matrix &operator*= (const matrix &r){
matrix ret(h, r.w);
for (int i = 0; i < h; i++){
for (int k = 0; k < w; k++){
for (int j = 0; j < r.w; j++){
ret.m[idx(i,j)] += m[idx(i,k)] * r.m[idx(k,j)];
}
}
}
return *this = ret;
}
matrix operator+ (const matrix &r) const { return matrix(*this) += r; }
matrix operator- (const matrix &r) const { return matrix(*this) -= r; }
matrix operator* (const matrix &r) const { return matrix(*this) *= r; }
matrix& operator*=(const T &r){
for (int i = 0; i < h; ++i){
for (int j = 0; j < w; ++j){
m[idx(i,j)] *= r;
}
}
return *this;
}
friend matrix operator* (const T &r, const matrix &mat){
return matrix(mat) *= r;
}
friend matrix operator* (const matrix &mat, const T &r){
return matrix(mat) *= r;
}
matrix pow(long long n){
if (n == 0) return e(h);
matrix f = pow(n / 2);
matrix ret = f * f;
if (n & 1) ret *= (*this);
return ret;
}
int idx(int i, int j){
return i * w + j;
}
static matrix e(int _h){
auto ret = matrix(_h, _h);
for (int i = 0; i < _h; i++){
ret[i][i] = T(1);
}
return ret;
}
friend std::ostream &operator<<(std::ostream &os, const matrix &mat){
for (int i = 0; i < mat.h; i++){
if (i != 0) os << '\n';
for (int j = 0; j < mat.w; j++){
if (j != 0) os << ' ';
os << mat[i][j];
}
}
return os;
}
friend std::istream &operator>>(std::istream &is, matrix &mat){
for (int i = 0; i < mat.h; i++){
for (int j = 0; j < mat.w; j++){
is >> mat[i][j];
}
}
return is;
}
};
template<typename T, size_t _hw = -1uz>
T determinant(matrix<T, _hw> mat){
int hw = mat.h;
T ret = 1;
for (int i = 0; i < hw; i++) {
int idx = -1;
for (int j = i; j < hw; j++) {
if (mat[j][i] != 0) {
idx = j;
break;
}
}
if (idx == -1) return 0;
if (i != idx) {
ret *= T(-1);
for (int j = 0; j < hw; j++){
std::swap(mat[i][j],mat[idx][j]);
}
}
ret *= mat[i][i];
T inv = T(1) / mat[i][i];
for (int j = 0; j < hw; j++) {
mat[i][j] *= inv;
}
for (int j = i + 1; j < hw; j++) {
T a = mat[j][i];
if (a == 0) continue;
for (int k = i; k < hw; k++) {
mat[j][k] -= mat[i][k] * a;
}
}
}
return ret;
}
} // namespace noya2
#line 2 "utility/modint.hpp"
#line 4 "utility/modint.hpp"
#line 2 "math/prime.hpp"
#line 4 "math/prime.hpp"
namespace noya2 {
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime_flag = is_prime_constexpr(n);
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u;
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root_flag = primitive_root_constexpr(m);
} // namespace noya2
#line 6 "utility/modint.hpp"
namespace noya2{
struct barrett {
unsigned int _m;
unsigned long long im;
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
unsigned long long z = a;
z *= b;
unsigned long long x = (unsigned long long)((__uint128_t(z) * im) >> 64);
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
template <int m>
struct static_modint {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
constexpr static_modint() : _v(0) {}
template<std::signed_integral T>
constexpr static_modint(T v){
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template<std::unsigned_integral T>
constexpr static_modint(T v){
_v = (unsigned int)(v % umod());
}
constexpr unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
constexpr mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
constexpr mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
constexpr mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (uint)(z % umod());
return *this;
}
constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
constexpr mint operator+() const { return *this; }
constexpr mint operator-() const { return mint() - *this; }
constexpr mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
constexpr mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend constexpr mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend constexpr mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend constexpr mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend constexpr mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend constexpr bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend constexpr bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
friend std::ostream &operator<<(std::ostream &os, const mint& p) {
return os << p.val();
}
friend std::istream &operator>>(std::istream &is, mint &a) {
long long t; is >> t;
a = mint(t);
return (is);
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = is_prime_flag<m>;
};
template <int id> struct dynamic_modint {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template<std::signed_integral T>
dynamic_modint(T v){
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template<std::unsigned_integral T>
dynamic_modint(T v){
_v = (unsigned int)(v % umod());
}
uint val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = noya2::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
friend std::ostream &operator<<(std::ostream &os, const mint& p) {
return os << p.val();
}
friend std::istream &operator>>(std::istream &is, mint &a) {
long long t; is >> t;
a = mint(t);
return (is);
}
private:
unsigned int _v;
static barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> noya2::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
template<typename T>
concept Modint = requires (T &a){
T::mod();
a.inv();
a.val();
a.pow(declval<int>());
};
} // namespace noya2
#line 8 "test/data_structure/Unionfind_with_Potential_NonCommutative_Group.test.cpp"
using mint = modint998244353;
using mat = matrix<mint,2>;
struct G {
using value_type = mat;
static mat op(mat a, mat b){
return a * b;
}
static mat e(){
return mat::e();
}
static mat inv(mat a){
return mat(array<mint,4uz>{a[1][1],-a[0][1],-a[1][0],a[0][0]});
}
};
int main(){
int n, q; in(n,q);
potentialized_dsu<G> d(n);
while (q--){
int t; in(t);
if (t == 0){
int u, v; in(u,v);
mat x; in(x);
int l = d.merge(u,v,x);
out(l == -1 ? 0 : 1);
}
if (t == 1){
int u, v; in(u,v);
if (d.same(u,v)){
mat x = d.diff(u,v);
out(x[0][0],x[0][1],x[1][0],x[1][1]);
}
else {
out(-1);
}
}
}
}