結果
問題 | No.3104 Simple Graph Problem |
ユーザー |
![]() |
提出日時 | 2025-02-12 06:58:02 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 185 ms / 2,000 ms |
コード長 | 44,605 bytes |
コンパイル時間 | 4,076 ms |
コンパイル使用メモリ | 329,520 KB |
実行使用メモリ | 26,784 KB |
最終ジャッジ日時 | 2025-02-12 06:58:18 |
合計ジャッジ時間 | 13,481 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 65 |
ソースコード
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp" using namespace std; #include<bits/stdc++.h> #line 1 "/Users/noya2/Desktop/Noya2_library/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 "/Users/noya2/Desktop/Noya2_library/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 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp" #line 6 "/Users/noya2/Desktop/Noya2_library/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 "/Users/noya2/Desktop/Noya2_library/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 2 "c.cpp" #line 2 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp" #line 4 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp" #line 2 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp" #line 4 "/Users/noya2/Desktop/Noya2_library/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); // constexpr long long primitive_root_constexpr(long long m){ // if (m == (1LL << 47) - (1LL << 24) + 1) return 3; // return primitive_root_constexpr(static_cast<int>(m)); // } } // namespace noya2 #line 6 "/Users/noya2/Desktop/Noya2_library/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 4 "c.cpp" using mint = modint998244353; #line 2 "/Users/noya2/Desktop/Noya2_library/graph/graph_query.hpp" #line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp" #line 4 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp" #include<ranges> #line 7 "/Users/noya2/Desktop/Noya2_library/data_structure/csr.hpp" namespace noya2::internal { template<class E> struct csr { csr () {} csr (int _n) : n(_n) {} csr (int _n, int m) : n(_n){ start.reserve(m); elist.reserve(m); } // ACL style constructor (do not have to call build) csr (int _n, const std::vector<std::pair<int,E>> &idx_elem) : n(_n), start(_n + 2), elist(idx_elem.size()) { for (auto &[i, e] : idx_elem){ start[i + 2]++; } for (int i = 1; i < n; i++){ start[i + 2] += start[i + 1]; } for (auto &[i, e] : idx_elem){ elist[start[i + 1]++] = e; } prepared = true; } int add(int idx, E elem){ int eid = start.size(); start.emplace_back(idx); elist.emplace_back(elem); return eid; } void build(){ if (prepared) return ; int m = start.size(); std::vector<E> nelist(m); std::vector<int> nstart(n + 2, 0); for (int i = 0; i < m; i++){ nstart[start[i] + 2]++; } for (int i = 1; i < n; i++){ nstart[i + 2] += nstart[i + 1]; } for (int i = 0; i < m; i++){ nelist[nstart[start[i] + 1]++] = elist[i]; } swap(elist,nelist); swap(start,nstart); prepared = true; } const auto operator[](int idx) const { return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]); } auto operator[](int idx){ return std::ranges::subrange(elist.begin()+start[idx],elist.begin()+start[idx+1]); } const auto operator()(int idx, int l, int r) const { return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r); } auto operator()(int idx, int l, int r){ return std::ranges::subrange(elist.begin()+start[idx]+l,elist.begin()+start[idx]+r); } size_t size() const { return n; } int n; std::vector<int> start; std::vector<E> elist; bool prepared = false; }; } // namespace noya2::internal #line 2 "/Users/noya2/Desktop/Noya2_library/graph/unweighted_type.hpp" namespace noya2 { struct unweighted {}; } // namespace noya2 #line 6 "/Users/noya2/Desktop/Noya2_library/graph/graph_query.hpp" #line 12 "/Users/noya2/Desktop/Noya2_library/graph/graph_query.hpp" namespace noya2 { template<typename Cost> struct graph { int n; internal::csr<std::pair<int,Cost>> g; Cost dist_inf = std::numeric_limits<Cost>::max() / 3; graph (int _n = 0) : n(_n), g(_n) {} graph (int _n, int _m) : n(_n), g(_n,_m) {} // 有向辺を追加 (無向辺ではないことに注意!) int add_edge(int u, int v, Cost cost = 1){ int id = g.add(u, {v,cost}); return id; } template<bool directed> static graph input(int _n, int _m, int indexed = 1){ if constexpr (directed){ graph g(_n, _m*2); for (int i = 0; i < _m; i++){ int u, v; std::cin >> u >> v; u -= indexed, v -= indexed; Cost c; std::cin >> c; g.add_edge(u, v, c); g.add_edge(v, u, c); } g.build(); return g; } else { graph g(_n, _m); for (int i = 0; i < _m; i++){ int u, v; std::cin >> u >> v; u -= indexed, v -= indexed; Cost c; std::cin >> c; g.add_edge(u, v, c); } g.build(); return g; } } void build(){ g.build(); } void set_inf(Cost new_inf){ dist_inf = new_inf; } std::vector<Cost> dijkstra(int s){ g.build(); std::vector<Cost> dist(n,dist_inf); dist[s] = 0; using P = std::pair<Cost,int>; std::priority_queue<P,std::vector<P>,std::greater<P>> pque; pque.push(P(0,s)); while (!pque.empty()){ auto [d, v] = pque.top(); pque.pop(); if (dist[v] < d) continue; for (auto [u, c] : g[v]){ if (chmin(dist[u],d+c)){ pque.push(P(dist[u],u)); } } } return dist; } std::vector<int> reconstruct(int s, int t, const std::vector<Cost> &dist){ if (dist[t] == dist_inf) return {}; g.build(); std::vector<int> from(n,-1); std::queue<int> que; que.push(s); while (!que.empty()){ int v = que.front(); que.pop(); for (auto [u, c] : g[v]){ if (from[u] == -1 && dist[u] == dist[v] + c){ from[u] = v; que.push(u); } } } std::vector<int> ans = {t}; while (t != s){ t = from[t]; ans.emplace_back(t); } std::reverse(ans.begin(),ans.end()); return ans; } std::vector<Cost> bfs01(int s){ g.build(); std::vector<Cost> dist(n,dist_inf); dist[s] = 0; std::deque<int> que; que.push_back(s); while (!que.empty()){ int v = que.front(); que.pop_front(); for (auto [u, c] : g[v]){ if (chmin(dist[u],dist[v]+c)){ if (c == 0) que.push_front(u); else que.push_back(u); } } } return dist; } std::vector<Cost> bfs1(int s){ g.build(); std::vector<Cost> dist(n,dist_inf); dist[s] = 0; std::queue<int> que; que.push(s); while (!que.empty()){ int v = que.front(); que.pop(); for (auto [u, c] : g[v]){ if (chmin(dist[u],dist[v]+c)){ que.push(u); } } } return dist; } std::vector<Cost> bellman_ford(int s, bool &ng_cycle){ g.build(); std::vector<Cost> dist(n,dist_inf); std::vector<int> ng; dist[s] = 0; int tm = 0; while (tm < n){ bool finish = true; for (int v = 0; v < n; v++){ if (dist[v] == dist_inf) continue; for (auto [u, c] : g[v]){ if (chmin(dist[u],dist[v]+c)){ finish = false; if (tm == n-1) ng.emplace_back(u); } } } if (finish) break; tm++; } ng_cycle = (tm == n); if (ng_cycle){ for (auto v : ng) dist[v] = -dist_inf; tm = n; while (tm--){ for (int v = 0; v < n; v++){ if (dist[v] != -dist_inf) continue; for (auto [u, c] : g[v]){ dist[u] = -dist_inf; } } } } return dist; } std::vector<std::vector<Cost>> warshall_floyd(){ g.build(); std::vector<std::vector<Cost>> dist(n,std::vector<Cost>(n,dist_inf)); for (int v = 0; v < n; v++){ dist[v][v] = 0; for (auto [u, c] : g[v]){ chmin(dist[v][u],c); } } for (int k = 0; k < n; k++){ for (int i = 0; i < n; i++){ for (int j = 0; j < n; j++){ chmin(dist[i][j],dist[i][k]+dist[k][j]); } } } return dist; } const auto operator[](int idx) const { return g[idx]; } auto operator[](int idx) { return g[idx]; } }; template<> struct graph<unweighted> { int n; internal::csr<int> g; int dist_inf = std::numeric_limits<int>::max() / 2; graph (int _n = 0) : n(_n), g(_n) {} graph (int _n, int _m) : n(_n), g(_n,_m) {} // 有向辺を追加 (無向辺ではないことに注意!) int add_edge(int u, int v){ int id = g.add(u, v); return id; } template<bool directed> static graph input(int _n, int _m, int indexed = 1){ if constexpr (directed){ graph g(_n, _m*2); for (int i = 0; i < _m; i++){ int u, v; std::cin >> u >> v; u -= indexed, v -= indexed; g.add_edge(u, v); g.add_edge(v, u); } g.build(); return g; } else { graph g(_n, _m); for (int i = 0; i < _m; i++){ int u, v; std::cin >> u >> v; u -= indexed, v -= indexed; g.add_edge(u, v); } g.build(); return g; } } void build(){ g.build(); } void set_inf(int new_inf){ dist_inf = new_inf; } std::vector<int> reconstruct(int s, int t, const std::vector<int> &dist){ if (dist[t] == dist_inf) return {}; g.build(); std::vector<int> from(n,-1); std::queue<int> que; que.push(s); while (!que.empty()){ int v = que.front(); que.pop(); for (auto u : g[v]){ if (from[u] == -1 && dist[u] == dist[v] + 1){ from[u] = v; que.push(u); } } } std::vector<int> ans = {t}; while (t != s){ t = from[t]; ans.emplace_back(t); } std::reverse(ans.begin(),ans.end()); return ans; } std::vector<int> bfs(int s){ g.build(); std::vector<int> dist(n,dist_inf); dist[s] = 0; std::queue<int> que; que.push(s); while (!que.empty()){ int v = que.front(); que.pop(); for (auto u : g[v]){ if (chmin(dist[u],dist[v]+1)){ que.push(u); } } } return dist; } const auto operator[](int idx) const { return g[idx]; } auto operator[](int idx) { return g[idx]; } }; template<> struct graph<bool> { int n; internal::csr<std::pair<int,bool>> g; int dist_inf = std::numeric_limits<int>::max() / 2; graph (int _n = 0) : n(_n), g(_n) {} graph (int _n, int _m) : n(_n), g(_n,_m) {} // 有向辺を追加 (無向辺ではないことに注意!) int add_edge(int u, int v, bool cost){ int id = g.add(u, {v, cost}); return id; } void build(){ g.build(); } void set_inf(int new_inf){ dist_inf = new_inf; } std::vector<int> reconstruct(int s, int t, const std::vector<int> &dist){ if (dist[t] == dist_inf) return {}; g.build(); std::vector<int> from(n,-1); std::queue<int> que; que.push(s); while (!que.empty()){ int v = que.front(); que.pop(); for (auto [u, b] : g[v]){ int c = (int)b; if (from[u] == -1 && dist[u] == dist[v] + c){ from[u] = v; que.push(u); } } } std::vector<int> ans = {t}; while (t != s){ t = from[t]; ans.emplace_back(t); } std::reverse(ans.begin(),ans.end()); return ans; } std::vector<int> bfs01(int s){ g.build(); std::vector<int> dist(n,dist_inf); dist[s] = 0; std::deque<int> que; que.push_back(s); while (!que.empty()){ int v = que.front(); que.pop_front(); for (auto [u, b] : g[v]){ int c = (int)b; if (chmin(dist[u],dist[v]+c)){ if (c == 0) que.push_front(u); else que.push_back(u); } } } return dist; } const auto operator[](int idx) const { return g[idx]; } auto operator[](int idx) { return g[idx]; } }; } // namespace noya2 #line 2 "/Users/noya2/Desktop/Noya2_library/tree/heavy_light_decomposition.hpp" #line 9 "/Users/noya2/Desktop/Noya2_library/tree/heavy_light_decomposition.hpp" #line 11 "/Users/noya2/Desktop/Noya2_library/tree/heavy_light_decomposition.hpp" namespace noya2 { struct hld_tree { int n, root; std::vector<int> down, nxt, sub, tour; noya2::internal::csr<int> childs; // default constructor (nop) hld_tree () {} // tree with _n node // after construct, call input_edges / input_parents / add_edge _n - 1 times hld_tree (int _n, int _root = 0) : n(_n), root(_root), down(n), nxt(n), sub(n, 1), tour(n) { if (n == 1){ nxt[0] = -1; down[0] = -1; build_from_parents(); } } // par[i] < i, par[0] == -1 hld_tree (const std::vector<int> &par) : n(par.size()), root(0), down(n, -1), nxt(par), sub(n, 1), tour(n){ build_from_parents(); } // par[i] < i, par[0] == -1 hld_tree (std::vector<int> &&par) : n(par.size()), root(0), down(n, -1), sub(n, 1), tour(n) { nxt.swap(par); build_from_parents(); } // distinct unweighted undirected n - 1 edges of tree hld_tree (const std::vector<std::pair<int, int>> &es, int _root = 0) : n(es.size() + 1), root(_root), down(n), nxt(n), sub(n, 1), tour(n) { for (auto &[u, v] : es){ down[u]++; down[v]++; nxt[u] ^= v; nxt[v] ^= u; } build_from_edges(); } // input parents from cin template<int indexed = 1> void input_parents(){ // using std::cin; nxt[0] = -1; for (int u = 1; u < n; u++){ cin >> nxt[u]; nxt[u] -= indexed; } build_from_parents(); } // input n - 1 edges from cin template<int indexed = 1> void input_edges(){ // using std::cin; for (int i = 1; i < n; i++){ int u, v; cin >> u >> v; u -= indexed; v -= indexed; down[u]++; down[v]++; nxt[u] ^= v; nxt[v] ^= u; } build_from_edges(); } void add_edge(int u, int v){ down[u]++; down[v]++; nxt[u] ^= v; nxt[v] ^= u; // use tour[0] as counter if (++tour[0] == n - 1){ build_from_edges(); } } size_t size() const { return n; } // top vertex of heavy path which contains v int leader(int v) const { return nxt[v] < 0 ? v : nxt[v]; } // level ancestor // ret is ancestor of v, dist(ret, v) == d // if d > depth(v), return -1 int la(int v, int d) const { while (v != -1){ int u = leader(v); if (down[v] - d >= down[u]){ v = tour[down[v] - d]; break; } d -= down[v] - down[u] + 1; v = (u == root ? -1 : ~nxt[u]); } return v; } // lowest common ancestor of u and v int lca(int u, int v) const { int du = down[u], dv = down[v]; if (du > dv){ std::swap(du, dv); std::swap(u, v); } if (dv < du + sub[u]){ return u; } while (du < dv){ v = ~nxt[leader(v)]; dv = down[v]; } return v; } // distance from u to v int dist(int u, int v) const { int _dist = 0; while (leader(u) != leader(v)){ if (down[u] > down[v]) std::swap(u, v); _dist += down[v] - down[leader(v)] + 1; v = ~nxt[leader(v)]; } _dist += std::abs(down[u] - down[v]); return _dist; } // d times move from to its neighbor (direction of to) // if d > dist(from, to), return -1 int jump(int from, int to, int d) const { int _from = from, _to = to; int dist_from_lca = 0, dist_to_lca = 0; while (leader(_from) != leader(_to)){ if (down[_from] > down[_to]){ dist_from_lca += down[_from] - down[leader(_from)] + 1; _from = ~nxt[leader(_from)]; } else { dist_to_lca += down[_to] - down[leader(_to)] + 1; _to = ~nxt[leader(_to)]; } } if (down[_from] > down[_to]){ dist_from_lca += down[_from] - down[_to]; } else { dist_to_lca += down[_to] - down[_from]; } if (d <= dist_from_lca){ return la(from, d); } d -= dist_from_lca; if (d <= dist_to_lca){ return la(to, dist_to_lca - d); } return -1; } // parent of v (if v is root, return -1) int parent(int v) const { if (v == root) return -1; return (nxt[v] < 0 ? ~nxt[v] : tour[down[v] - 1]); } // visiting time in euler tour // usage : seg.set(index(v), X[v]) int index(int vertex) const { return down[vertex]; } // usage : seg.set(index_edge(e.u, e.v), e.val) int index(int vertex1, int vertex2) const { return std::max(down[vertex1], down[vertex2]); } // subtree size of v int subtree_size(int v) const { return sub[v]; } // prod in subtree v : seg.prod(subtree_l(v), subtree_r(v)) int subtree_l(int v) const { return down[v]; } int subtree_r(int v) const { return down[v] + sub[v]; } // v is in subtree r bool is_in_subtree(int r, int v) const { return subtree_l(r) <= subtree_l(v) && subtree_r(v) <= subtree_r(r); } // distance table from s std::vector<int> dist_table(int s) const { std::vector<int> table(n, -1); table[s] = 0; while (s != root){ table[parent(s)] = table[s] + 1; s = parent(s); } for (int v : tour){ if (table[v] == -1){ table[v] = table[parent(v)] + 1; } } return table; } // dist, v1, v2 std::tuple<int, int, int> diameter() const { std::vector<int> dep = dist_table(root); int v1 = std::ranges::max_element(dep) - dep.begin(); std::vector<int> fromv1 = dist_table(v1); int v2 = std::ranges::max_element(fromv1) - fromv1.begin(); return {fromv1[v2], v1, v2}; } // vertex array {from, ..., to} std::vector<int> path(int from, int to) const { int d = dist(from, to); std::vector<int> _path(d + 1); int front = 0, back = d; while (from != to){ if (down[from] > down[to]){ _path[front++] = from; from = parent(from); } else { _path[back--] = to; to = parent(to); } } _path[front] = from; return _path; } // path decomposition and query (vertex weighted) // if l < r, decsending order tour[l, r) // if l > r, acsending order tour(l, r] template<bool vertex = true> void path_query(int u, int v, auto f) const { while (leader(u) != leader(v)){ if (down[u] < down[v]){ f(down[leader(v)], down[v] + 1); v = ~nxt[leader(v)]; } else { f(down[u] + 1, down[leader(u)]); u = ~nxt[leader(u)]; } } if constexpr (vertex){ if (down[u] < down[v]){ f(down[u], down[v] + 1); } else { f(down[u] + 1, down[v]); } } else { if (down[u] != down[v]){ f(down[u] + 1, down[v] + 1); } } } // {parent, mapping} : cptree i is correspond to tree mapping[i]. parent[i] is parent of i in cptree. // parent[i] < i, parent[0] == -1 std::pair<std::vector<int>, std::vector<int>> compressed_tree(std::vector<int> vs) const { if (vs.empty()){ return {{},{}}; } auto comp = [&](int l, int r){ return down[l] < down[r]; }; std::ranges::sort(vs, comp); int sz = vs.size(); vs.reserve(2*sz); for (int i = 0; i < sz-1; i++){ vs.emplace_back(lca(vs[i], vs[i+1])); } std::sort(vs.begin() + sz, vs.end(), comp); std::ranges::inplace_merge(vs, vs.begin() + sz, comp); auto del = std::ranges::unique(vs); vs.erase(del.begin(), del.end()); sz = vs.size(); std::stack<int> st; std::vector<int> par(sz); par[0] = -1; st.push(0); for (int i = 1; i < sz; i++){ while (!is_in_subtree(vs[st.top()], vs[i])) st.pop(); par[i] = st.top(); st.push(i); } return {par, vs}; } //* CSR // build csr for using operator() void build_csr(){ childs = noya2::internal::csr<int>(n, n - 1); for (int v = 0; v < n; v++){ if (v == root) continue; if (leader(v) != v){ childs.add(parent(v),v); } } for (int v = 0; v < n; v++){ if (v == root) continue; if (leader(v) == v){ childs.add(parent(v),v); } } childs.build(); } const auto operator()(int v) const { return childs[v]; } auto operator()(int v){ return childs[v]; } //*/ // hld_tree g; // euler tour order : `for (int v : g)` // with range_adaptor : `for (int v : g | std::views::reverse)` // bottom-up DP : `for (int v : g | std::views::drop(1) | std::views::reverse){ update dp[g.parent(v)] by dp[v] }` auto begin() const { return tour.begin(); } auto end() const { return tour.end(); } private: // nxt[v] : parent of v, nxt[0] == -1 void build_from_parents(){ for (int u = n - 1; u >= 1; u--){ int v = nxt[u]; sub[v] += sub[u]; down[v] = std::max(down[v], sub[u]); } for (int u = n - 1; u >= 1; u--){ int v = nxt[u]; if (down[v] == sub[u]){ sub[u] = ~sub[u]; down[v] = ~down[v]; } } sub[0] = ~down[0] + 1; down[0] = 0; for (int u = 1; u < n; u++){ int v = nxt[u]; int nsub = ~down[u] + 1; if (sub[u] < 0){ down[u] = down[v] + 1; nxt[u] = (nxt[v] < 0 ? v : nxt[v]); } else { down[u] = down[v] + sub[v]; sub[v] += sub[u]; nxt[u] = ~v; } sub[u] = nsub; } for (int u = 0; u < n; u++){ tour[down[u]] = u; } } // down[v] : degree of v // nxt[v] : xor prod of neighbor of v void build_from_edges(){ // use tour as queue int back = 0; for (int u = 0; u < n; u++){ if (u != root && down[u] == 1){ tour[back++] = u; } } for (int front = 0; front < n - 1; front++){ int u = tour[front]; down[u] = -1; int v = nxt[u]; // parent of v nxt[v] ^= u; if (--down[v] == 1 && v != root){ tour[back++] = v; } } // check : now, tour is reverse of topological order tour.pop_back(); // check : now, down[*] <= 1 for (int u : tour){ int v = nxt[u]; // subtree size (initialized (1,1,...,1)) sub[v] += sub[u]; // heaviest subtree of its child down[v] = std::max(down[v], sub[u]); } for (int u : tour){ int v = nxt[u]; // whether u is not the top of heavy path if (down[v] == sub[u]){ sub[u] = ~sub[u]; down[v] = ~down[v]; } } // after appearing v as u (or v == root), // down[v] is the visiting time of euler tour // nxt[v] is the lowest vertex of heavy path which contains v // (if v itself, nxt[v] is ~(parent of v)) // sub[v] + down[v] is the light child's starting time of euler tour // note : heavy child's visiting time of euler tour is (the time of its parent) + 1 sub[root] = ~down[root] + 1; down[root] = 0; nxt[root] = -1; for (int u : tour | std::views::reverse){ int v = nxt[u]; int nsub = ~down[u] + 1; // heavy child if (sub[u] < 0){ down[u] = down[v] + 1; nxt[u] = (nxt[v] < 0 ? v : nxt[v]); } // light child else { down[u] = down[v] + sub[v]; sub[v] += sub[u]; nxt[u] = ~v; } sub[u] = nsub; } // tour is inverse permutation of down tour.push_back(0); for (int u = 0; u < n; u++){ tour[down[u]] = u; } } }; } // namespace noya2 #line 7 "c.cpp" #line 2 "/Users/noya2/Desktop/Noya2_library/data_structure/dsu.hpp" #line 6 "/Users/noya2/Desktop/Noya2_library/data_structure/dsu.hpp" namespace noya2{ struct dsu { public: dsu() : _n(0) {} dsu(int n) : _n(n), parent_or_size(n, -1) {} int merge(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); int x = leader(a), y = leader(b); if (x == y) return x; if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y); parent_or_size[x] += parent_or_size[y]; parent_or_size[y] = x; return x; } bool same(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); return leader(a) == leader(b); } int leader(int a) { assert(0 <= a && a < _n); if (parent_or_size[a] < 0) return a; return parent_or_size[a] = leader(parent_or_size[a]); } int size(int a) { assert(0 <= a && a < _n); return -parent_or_size[leader(a)]; } 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; // root node: -1 * component size // otherwise: parent std::vector<int> parent_or_size; }; } // namespace noya2 #line 9 "c.cpp" void solve(){ int n, m; in(n,m); vector<mint> a(n); in(a); graph<int> g(n); vector<pii> es(m); rep(i,m){ int u, v; in(u,v); u--, v--; g.add_edge(u,v,i); g.add_edge(v,u,i); es[i] = {u,v}; } g.build(); hld_tree ug(n); { dsu d(n); for (auto [u, v] : es){ if (d.same(u,v)) continue; d.merge(u,v); ug.add_edge(u,v); } } vector<int> dep = ug.dist_table(0); int esame = [&]{ rep(v,n) for (auto [u, i] : g[v]){ if (dep[v] % 2 == dep[u] % 2){ return i; } } return -1; }(); // bipartite if (esame == -1){ dsu d(n); vector<mint> ans(m); graph<int> tr(n); rep(i,m){ auto [u, v] = es[i]; if (d.same(u,v)) continue; tr.add_edge(u,v,i); tr.add_edge(v,u,i); d.merge(u,v); } tr.build(); auto dfs = [&](auto sfs, int v, int f) -> void { for (auto [u, i] : tr[v]){ if (u == f) continue; sfs(sfs,u,v); ans[i] = a[u]; a[u] -= ans[i]; a[v] -= ans[i]; } }; dfs(dfs,0,-1); if (a[0].val() != 0){ out(-1); return ; } out(ans); return ; } // not bipartite auto aa = a; auto [v0, v1] = es[esame]; vector<int> p01 = ug.path(v0,v1); vector<mint> ans(m); dsu d(n); int sz = p01.size(); map<pii,int> eid; rep(v,n) for (auto [u, i] : g[v]){ eid[pii(u,v)] = i; } vector<int> ids; rep(i,sz-1){ d.merge(p01[i],p01[i+1]); ids.emplace_back(eid[pii(p01[i],p01[i+1])]); } ids.emplace_back(eid[pii(v1,v0)]); graph<int> tr(n); rep(i,m){ auto [u, v] = es[i]; if (d.same(u,v)) continue; tr.add_edge(u,v,i); tr.add_edge(v,u,i); d.merge(u,v); } tr.build(); auto dfs = [&](auto sfs, int v, int f) -> void { for (auto [u, i] : tr[v]){ if (u == f) continue; sfs(sfs,u,v); ans[i] = a[u]; a[u] -= ans[i]; a[v] -= ans[i]; } }; for (int p : p01){ dfs(dfs,p,-1); } mint buf = 0; for (int p : p01){ buf = -buf + a[p]; } mint x = buf / 2; ans[ids.back()] = x; buf = 0; rep(i,sz-1){ buf = -buf + a[p01[i]]; ans[ids[i]] = buf - x; x = -x; } out(ans); // out(sz); // rep(i,m){ // auto [u, v] = es[i]; // aa[u] -= ans[i]; // aa[v] -= ans[i]; // } // out(aa); cout << flush; // rep(i,n){ // assert(aa[i].val() == 0); // } } int main(){ int t = 1; //in(t); while (t--) { solve(); } }