結果
| 問題 |
No.1207 グラフX
|
| コンテスト | |
| ユーザー |
 maspy
|
| 提出日時 | 2022-05-13 00:23:13 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 174 ms / 2,000 ms |
| コード長 | 41,144 bytes |
| コンパイル時間 | 2,776 ms |
| コンパイル使用メモリ | 227,760 KB |
| 最終ジャッジ日時 | 2025-01-29 06:21:32 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 46 |
ソースコード
#line 1 "/home/maspy/compro/library/my_template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pi = pair<ll, ll>;
using vi = vector<ll>;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define vv(type, name, h, ...) \
vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
vector<vector<vector<type>>> name( \
h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name( \
a, vector<vector<vector<type>>>( \
b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll i = 0; i < ll(a); ++i)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define FOR4_R(i, a, b, c) for (ll i = (b)-1; i >= ll(a); i -= (c))
#define overload4(a, b, c, d, e, ...) e
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) \
overload4(__VA_ARGS__, FOR4_R, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) for (ll t = s; t >= 0; t = (t == 0 ? -1 : (t - 1) & s))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
template <typename T>
T SUM(vector<T> &A) {
T sum = T(0);
for (auto &&a: A) sum += a;
return sum;
}
template <class... T>
constexpr auto min(T... a) {
return min(initializer_list<common_type_t<T...>>{a...});
}
template <class... T>
constexpr auto max(T... a) {
return max(initializer_list<common_type_t<T...>>{a...});
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T, typename U>
T ceil(T x, U y) {
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
T q = floor(x, y);
return {q, x - q * y};
}
ll binary_search(function<bool(ll)> check, ll ok, ll ng) {
assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
if (check(x))
ok = x;
else
ng = x;
}
return ok;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
vi s_to_vi(const string &S, char first_char) {
vi A(S.size());
FOR(i, S.size()) { A[i] = S[i] - first_char; }
return A;
}
template <typename T>
vector<T> cumsum(vector<T> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
template <typename CNT, typename T>
vc<CNT> bincount(const vc<T> &A, int size) {
vc<CNT> C(size);
for (auto &&x: A) { ++C[x]; }
return C;
}
template <typename T>
vector<int> argsort(const vector<T> &A) {
// stable
vector<int> ids(A.size());
iota(all(ids), 0);
sort(all(ids),
[&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
int n = len(A);
assert(len(I) == n);
vc<T> B(n);
FOR(i, n) B[i] = A[I[i]];
return B;
}
#line 1 "/home/maspy/compro/library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>
namespace detail {
template <typename T, decltype(&T::is_modint) = &T::is_modint>
std::true_type check_value(int);
template <typename T>
std::false_type check_value(long);
} // namespace detail
template <typename T>
struct is_modint : decltype(detail::check_value<T>(0)) {};
template <typename T>
using is_modint_t = enable_if_t<is_modint<T>::value>;
template <typename T>
using is_not_modint_t = enable_if_t<!is_modint<T>::value>;
struct Scanner {
FILE *fp;
char line[(1 << 15) + 1];
size_t st = 0, ed = 0;
void reread() {
memmove(line, line + st, ed - st);
ed -= st;
st = 0;
ed += fread(line + ed, 1, (1 << 15) - ed, fp);
line[ed] = '\0';
}
bool succ() {
while (true) {
if (st == ed) {
reread();
if (st == ed) return false;
}
while (st != ed && isspace(line[st])) st++;
if (st != ed) break;
}
if (ed - st <= 50) {
bool sep = false;
for (size_t i = st; i < ed; i++) {
if (isspace(line[i])) {
sep = true;
break;
}
}
if (!sep) reread();
}
return true;
}
template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
bool read_single(T &ref) {
if (!succ()) return false;
while (true) {
size_t sz = 0;
while (st + sz < ed && !isspace(line[st + sz])) sz++;
ref.append(line + st, sz);
st += sz;
if (!sz || st != ed) break;
reread();
}
return true;
}
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
bool read_single(T &ref) {
if (!succ()) return false;
bool neg = false;
if (line[st] == '-') {
neg = true;
st++;
}
ref = T(0);
while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
if (neg) ref = -ref;
return true;
}
template <class T, is_modint_t<T> * = nullptr>
bool read_single(T &ref) {
long long val = 0;
bool f = read_single(val);
ref = T(val);
return f;
}
bool read_single(double &ref) {
string s;
if (!read_single(s)) return false;
ref = std::stod(s);
return true;
}
bool read_single(char &ref) {
string s;
if (!read_single(s) || s.size() != 1) return false;
ref = s[0];
return true;
}
template <class T>
bool read_single(vector<T> &ref) {
for (auto &d: ref) {
if (!read_single(d)) return false;
}
return true;
}
template <class T, class U>
bool read_single(pair<T, U> &p) {
return (read_single(p.first) && read_single(p.second));
}
template <class A, class B, class C>
bool read_single(tuple<A, B, C> &p) {
return (read_single(get<0>(p)) && read_single(get<1>(p))
&& read_single(get<2>(p)));
}
template <class A, class B, class C, class D>
bool read_single(tuple<A, B, C, D> &p) {
return (read_single(get<0>(p)) && read_single(get<1>(p))
&& read_single(get<2>(p)) && read_single(get<3>(p)));
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
bool f = read_single(h);
assert(f);
read(t...);
}
Scanner(FILE *fp) : fp(fp) {}
};
struct Printer {
Printer(FILE *_fp) : fp(_fp) {}
~Printer() { flush(); }
static constexpr size_t SIZE = 1 << 15;
FILE *fp;
char line[SIZE], small[50];
size_t pos = 0;
void flush() {
fwrite(line, 1, pos, fp);
pos = 0;
}
void write(const char &val) {
if (pos == SIZE) flush();
line[pos++] = val;
}
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
void write(T val) {
if (pos > (1 << 15) - 50) flush();
if (val == 0) {
write('0');
return;
}
if (val < 0) {
write('-');
val = -val; // todo min
}
size_t len = 0;
while (val) {
small[len++] = char(0x30 | (val % 10));
val /= 10;
}
for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
pos += len;
}
void write(const string &s) {
for (char c: s) write(c);
}
void write(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) write(s[i]);
}
void write(const double &x) {
ostringstream oss;
oss << setprecision(15) << x;
string s = oss.str();
write(s);
}
void write(const long double &x) {
ostringstream oss;
oss << setprecision(15) << x;
string s = oss.str();
write(s);
}
template <class T, is_modint_t<T> * = nullptr>
void write(T &ref) {
write(ref.val);
}
template <class T>
void write(const vector<T> &val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) write(' ');
write(val[i]);
}
}
template <class T, class U>
void write(const pair<T, U> &val) {
write(val.first);
write(' ');
write(val.second);
}
template <class A, class B, class C>
void write(const tuple<A, B, C> &val) {
auto &[a, b, c] = val;
write(a), write(' '), write(b), write(' '), write(c);
}
template <class A, class B, class C, class D>
void write(const tuple<A, B, C, D> &val) {
auto &[a, b, c, d] = val;
write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d);
}
template <class A, class B, class C, class D, class E>
void write(const tuple<A, B, C, D, E> &val) {
auto &[a, b, c, d, e] = val;
write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e);
}
template <class A, class B, class C, class D, class E, class F>
void write(const tuple<A, B, C, D, E, F> &val) {
auto &[a, b, c, d, e, f] = val;
write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e), write(' '), write(f);
}
template <class T, size_t S>
void write(const array<T, S> &val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) write(' ');
write(val[i]);
}
}
void write(i128 val) {
string s;
bool negative = 0;
if(val < 0){
negative = 1;
val = -val;
}
while (val) {
s += '0' + int(val % 10);
val /= 10;
}
if(negative) s += "-";
reverse(all(s));
if (len(s) == 0) s = "0";
write(s);
}
};
Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);
void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
printer.write(head);
if (sizeof...(Tail)) printer.write(' ');
print(forward<Tail>(tail)...);
}
void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
scanner.read(head);
read(tail...);
}
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 2 "/home/maspy/compro/library/graph/base.hpp"
template <typename T>
struct Edge {
int frm, to;
T cost;
int id;
};
template <typename T = int, bool directed = false>
struct Graph {
int N, M;
using cost_type = T;
using edge_type = Edge<T>;
vector<edge_type> edges;
vector<int> indptr;
vector<edge_type> csr_edges;
bool prepared;
class OutgoingEdges {
public:
OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}
const edge_type* begin() const {
if (l == r) { return 0; }
return &G->csr_edges[l];
}
const edge_type* end() const {
if (l == r) { return 0; }
return &G->csr_edges[r];
}
private:
int l, r;
const Graph* G;
};
bool is_prepared() { return prepared; }
constexpr bool is_directed() { return directed; }
Graph() : N(0), M(0), prepared(0) {}
Graph(int N) : N(N), M(0), prepared(0) {}
void add(int frm, int to, T cost = 1, int i = -1) {
assert(!prepared && 0 <= frm && 0 <= to && to < N);
if (i == -1) i = M;
auto e = edge_type({frm, to, cost, i});
edges.eb(e);
++M;
}
// wt, off
void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }
void read_graph(int M, bool wt = false, int off = 1) {
FOR(M) {
INT(a, b);
a -= off, b -= off;
if (!wt) {
add(a, b);
} else {
T c;
read(c);
add(a, b, c);
}
}
build();
}
void read_parent(int off = 1) {
FOR3(v, 1, N) {
INT(p);
p -= off;
add(p, v);
}
build();
}
void build() {
assert(!prepared);
prepared = true;
indptr.assign(N + 1, 0);
for (auto&& e: edges) {
indptr[e.frm + 1]++;
if (!directed) indptr[e.to + 1]++;
}
FOR(v, N) indptr[v + 1] += indptr[v];
auto counter = indptr;
csr_edges.resize(indptr.back() + 1);
for (auto&& e: edges) {
csr_edges[counter[e.frm]++] = e;
if (!directed)
csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
}
}
OutgoingEdges operator[](int v) const {
assert(prepared);
return {this, indptr[v], indptr[v + 1]};
}
void debug() {
print("Graph");
if (!prepared) {
print("frm to cost id");
for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);
} else {
print("indptr", indptr);
print("frm to cost id");
FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);
}
}
};
#line 2 "/home/maspy/compro/library/mod/modint.hpp"
template <u32 mod>
struct modint {
static constexpr bool is_modint = true;
u32 val;
constexpr modint(const ll val = 0) noexcept
: val(val >= 0 ? val % mod : (mod - (-val) % mod) % mod) {}
bool operator<(const modint &other) const {
return val < other.val;
} // To use std::map
modint &operator+=(const modint &p) {
if ((val += p.val) >= mod) val -= mod;
return *this;
}
modint &operator-=(const modint &p) {
if ((val += mod - p.val) >= mod) val -= mod;
return *this;
}
modint &operator*=(const modint &p) {
val = (u32)(1LL * val * p.val % mod);
return *this;
}
modint &operator/=(const modint &p) {
*this *= p.inverse();
return *this;
}
modint operator-() const { return modint(get_mod() - val); }
modint operator+(const modint &p) const { return modint(*this) += p; }
modint operator-(const modint &p) const { return modint(*this) -= p; }
modint operator*(const modint &p) const { return modint(*this) *= p; }
modint operator/(const modint &p) const { return modint(*this) /= p; }
bool operator==(const modint &p) const { return val == p.val; }
bool operator!=(const modint &p) const { return val != p.val; }
modint inverse() const {
int a = val, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
return modint(u);
}
modint pow(int64_t n) const {
modint ret(1), mul(val);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
static constexpr u32 get_mod() { return mod; }
};
struct ArbitraryModInt {
static constexpr bool is_modint = true;
u32 val;
ArbitraryModInt() : val(0) {}
ArbitraryModInt(int64_t y)
: val(y >= 0 ? y % get_mod()
: (get_mod() - (-y) % get_mod()) % get_mod()) {}
bool operator<(const ArbitraryModInt &other) const {
return val < other.val;
} // To use std::map<ArbitraryModInt, T>
static u32 &get_mod() {
static u32 mod = 0;
return mod;
}
static void set_mod(int md) { get_mod() = md; }
ArbitraryModInt &operator+=(const ArbitraryModInt &p) {
if ((val += p.val) >= get_mod()) val -= get_mod();
return *this;
}
ArbitraryModInt &operator-=(const ArbitraryModInt &p) {
if ((val += get_mod() - p.val) >= get_mod()) val -= get_mod();
return *this;
}
ArbitraryModInt &operator*=(const ArbitraryModInt &p) {
unsigned long long a = (unsigned long long)val * p.val;
unsigned xh = (unsigned)(a >> 32), xl = (unsigned)a, d, m;
asm("divl %4; \n\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(get_mod()));
val = m;
return *this;
}
ArbitraryModInt &operator/=(const ArbitraryModInt &p) {
*this *= p.inverse();
return *this;
}
ArbitraryModInt operator-() const { return ArbitraryModInt(get_mod() - val); }
ArbitraryModInt operator+(const ArbitraryModInt &p) const {
return ArbitraryModInt(*this) += p;
}
ArbitraryModInt operator-(const ArbitraryModInt &p) const {
return ArbitraryModInt(*this) -= p;
}
ArbitraryModInt operator*(const ArbitraryModInt &p) const {
return ArbitraryModInt(*this) *= p;
}
ArbitraryModInt operator/(const ArbitraryModInt &p) const {
return ArbitraryModInt(*this) /= p;
}
bool operator==(const ArbitraryModInt &p) const { return val == p.val; }
bool operator!=(const ArbitraryModInt &p) const { return val != p.val; }
ArbitraryModInt inverse() const {
int a = val, b = get_mod(), u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
return ArbitraryModInt(u);
}
ArbitraryModInt pow(int64_t n) const {
ArbitraryModInt ret(1), mul(val);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
};
template <typename mint>
tuple<mint, mint, mint> get_factorial_data(int n) {
static const int mod = mint::get_mod();
assert(0 <= n && n < mod);
static vector<mint> fact = {1, 1};
static vector<mint> fact_inv = {1, 1};
static vector<mint> inv = {0, 1};
while (len(fact) <= n) {
int k = len(fact);
fact.eb(fact[k - 1] * mint(k));
auto q = ceil(mod, k);
int r = k * q - mod;
inv.eb(inv[r] * mint(q));
fact_inv.eb(fact_inv[k - 1] * inv[k]);
}
return {fact[n], fact_inv[n], inv[n]};
}
template <typename mint>
mint fact(int n) {
static const int mod = mint::get_mod();
assert(0 <= n);
if (n >= mod) return 0;
return get<0>(get_factorial_data<mint>(n));
}
template <typename mint>
mint fact_inv(int n) {
static const int mod = mint::get_mod();
assert(0 <= n && n < mod);
return get<1>(get_factorial_data<mint>(n));
}
template <typename mint>
mint inv(int n) {
static const int mod = mint::get_mod();
assert(0 <= n && n < mod);
return get<2>(get_factorial_data<mint>(n));
}
template <typename mint, bool large = false>
mint C(ll n, ll k) {
assert(n >= 0);
if (k < 0 || n < k) return 0;
if (!large) return fact<mint>(n) * fact_inv<mint>(k) * fact_inv<mint>(n - k);
k = min(k, n - k);
mint x(1);
FOR(i, k) { x *= mint(n - i); }
x *= fact_inv<mint>(k);
return x;
}
template <typename mint, bool large = false>
mint C_inv(ll n, ll k) {
assert(n >= 0);
assert(0 <= k && k <= n);
if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
return mint(1) / C<mint, 1>(n, k);
}
using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
using amint = ArbitraryModInt;
#line 2 "/home/maspy/compro/library/ds/unionfind.hpp"
struct UnionFind {
int num;
int comp;
vc<int> size, par;
UnionFind(int n) : num(n), comp(n), size(n, 1), par(n) {
iota(par.begin(), par.end(), 0);
}
int find(int x) {
while (par[x] != x) {
par[x] = par[par[x]];
x = par[x];
}
return x;
}
int operator[](int x) { return find(x); }
bool merge(ll x, ll y) {
x = find(x);
y = find(y);
if (x == y) { return false; }
comp--;
if (size[x] < size[y]) swap(x, y);
size[x] += size[y];
size[y] = 0;
par[y] = x;
return true;
}
vc<int> find_all() {
vc<int> A(num);
FOR(i, num) A[i] = find(i);
return A;
}
void reset(){
comp = num;
size.assign(num, 1);
iota(all(par), 0);
}
};
#line 3 "/home/maspy/compro/library/graph/hld.hpp"
/*
HL分解。O(N) 時間構築。
LCA, LA などは O(logN) 時間。
木以外、非連結でも使えるようにした。dfs順序や親がとれる。
*/
template <typename Graph>
struct HLD {
Graph &G;
int N;
vector<int> LID, RID, head, V, parent, root;
vc<ll> depth;
vector<bool> in_tree;
HLD(Graph &G, int r = -1)
: G(G),
N(G.N),
LID(G.N),
RID(G.N),
head(G.N, r),
V(G.N),
parent(G.N, -1),
depth(G.N, -1),
root(G.N, -1),
in_tree(G.M, 0) {
assert(G.is_prepared());
int t1 = 0;
if (r != -1) {
dfs_sz(r, -1);
dfs_hld(r, t1);
} else {
FOR(r, N) if (parent[r] == -1) {
head[r] = r;
dfs_sz(r, -1);
dfs_hld(r, t1);
}
}
for (auto &&v: V) root[v] = (parent[v] == -1 ? v : root[parent[v]]);
}
void dfs_sz(int v, int p) {
auto &sz = RID;
parent[v] = p;
depth[v] = (p == -1 ? 0 : depth[p] + 1);
sz[v] = 1;
int l = G.indptr[v], r = G.indptr[v + 1];
auto &csr = G.csr_edges;
// 使う辺があれば先頭にする
FOR3_R(i, l, r - 1) {
if (depth[csr[i + 1].to] == -1) swap(csr[i], csr[i + 1]);
}
int hld_sz = 0;
for (int i = l; i < r; ++i) {
auto e = csr[i];
if (depth[e.to] != -1) continue;
in_tree[e.id] = 1;
dfs_sz(e.to, v);
sz[v] += sz[e.to];
if (chmax(hld_sz, sz[e.to]) && l < i) { swap(csr[l], csr[i]); }
}
}
void dfs_hld(int v, int ×) {
LID[v] = times++;
RID[v] += LID[v];
V[LID[v]] = v;
bool heavy = true;
for (auto &&e: G[v]) {
if (!in_tree[e.id] || depth[e.to] <= depth[v]) continue;
head[e.to] = (heavy ? head[v] : e.to);
heavy = false;
dfs_hld(e.to, times);
}
}
int e_to_v(int eid) {
auto e = G.edges[eid];
return (parent[e.frm] == e.to ? e.frm : e.to);
}
int ELID(int v) { return 2 * LID[v] - depth[v]; }
int ERID(int v) { return 2 * RID[v] - depth[v] - 1; }
/* k: 0-indexed */
int LA(int v, int k) {
while (1) {
int u = head[v];
if (LID[v] - k >= LID[u]) return V[LID[v] - k];
k -= LID[v] - LID[u] + 1;
v = parent[u];
}
}
int LCA(int u, int v) {
for (;; v = parent[head[v]]) {
if (LID[u] > LID[v]) swap(u, v);
if (head[u] == head[v]) return u;
}
}
int lca(int u, int v) { return LCA(u, v); }
int la(int u, int v) { return LA(u, v); }
int subtree_size(int v) { return RID[v] - LID[v]; }
int dist(int a, int b) {
int c = LCA(a, b);
return depth[a] + depth[b] - 2 * depth[c];
}
bool in_subtree(int a, int b) { return LID[b] <= LID[a] && LID[a] < RID[b]; }
int move(int a, int b) {
assert(a != b);
return (in_subtree(b, a) ? LA(b, depth[b] - depth[a] - 1) : parent[a]);
}
vc<int> collect_child(int v) {
vc<int> res;
for (auto &&e: G[v])
if (e.to != parent[v]) res.eb(e.to);
return res;
}
vc<pair<int, int>> get_path_decomposition(int u, int v, bool edge) {
// [始点, 終点] の"閉"区間列。
vc<pair<int, int>> up, down;
while (1) {
if (head[u] == head[v]) break;
if (LID[u] < LID[v]) {
down.eb(LID[head[v]], LID[v]);
v = parent[head[v]];
} else {
up.eb(LID[u], LID[head[u]]);
u = parent[head[u]];
}
}
if (LID[u] < LID[v]) down.eb(LID[u] + edge, LID[v]);
elif (LID[v] + edge <= LID[u]) up.eb(LID[u], LID[v] + edge);
reverse(all(down));
up.insert(up.end(), all(down));
return up;
}
void debug() {
print("V", V);
print("LID", LID);
print("RID", RID);
print("parent", parent);
print("depth", depth);
print("head", head);
print("in_tree(edge)", in_tree);
print("root", root);
}
};
#line 2 "/home/maspy/compro/library/ds/segtree.hpp"
template <class Monoid>
struct SegTree {
using X = typename Monoid::value_type;
using value_type = X;
vc<X> dat;
int n, log, size;
SegTree() : SegTree(0) {}
SegTree(int n) : SegTree(vc<X>(n, Monoid::unit())) {}
SegTree(vc<X> v) : n(len(v)) {
log = 1;
while ((1 << log) < n) ++log;
size = 1 << log;
dat.assign(size << 1, Monoid::unit());
FOR(i, n) dat[size + i] = v[i];
FOR3_R(i, 1, size) update(i);
}
void reset() { fill(all(dat), Monoid::unit()); }
void set_all(const vc<X>& v){
dat.assign(size << 1, Monoid::unit());
FOR(i, n) dat[size + i] = v[i];
FOR3_R(i, 1, size) update(i);
}
X operator[](int i) { return dat[size + i]; }
void update(int i) { dat[i] = Monoid::op(dat[2 * i], dat[2 * i + 1]); }
void set(int i, X x) {
assert(i < n);
dat[i += size] = x;
while (i >>= 1) update(i);
}
X prod(int L, int R) {
assert(L <= R);
assert(R <= n);
X vl = Monoid::unit(), vr = Monoid::unit();
L += size, R += size;
while (L < R) {
if (L & 1) vl = Monoid::op(vl, dat[L++]);
if (R & 1) vr = Monoid::op(dat[--R], vr);
L >>= 1, R >>= 1;
}
return Monoid::op(vl, vr);
}
X prod_all() { return dat[1]; }
template <class F>
int max_right(F &check, int L) {
assert(0 <= L && L <= n && check(Monoid::unit()));
if (L == n) return n;
L += size;
X sm = Monoid::unit();
do {
while (L % 2 == 0) L >>= 1;
if (!check(Monoid::op(sm, dat[L]))) {
while (L < size) {
L = 2 * L;
if (check(Monoid::op(sm, dat[L]))) {
sm = Monoid::op(sm, dat[L]);
L++;
}
}
return L - size;
}
sm = Monoid::op(sm, dat[L]);
L++;
} while ((L & -L) != L);
return n;
}
template <class F>
int min_left(F &check, int R) {
assert(0 <= R && R <= n && check(Monoid::unit()));
if (R == 0) return 0;
R += size;
X sm = Monoid::unit();
do {
--R;
while (R > 1 && (R % 2)) R >>= 1;
if (!check(Monoid::op(dat[R], sm))) {
while (R < size) {
R = 2 * R + 1;
if (check(Monoid::op(dat[R], sm))) {
sm = Monoid::op(dat[R], sm);
R--;
}
}
return R + 1 - size;
}
sm = Monoid::op(dat[R], sm);
} while ((R & -R) != R);
return 0;
}
// モノイドが可換なら、prod_{l<=i<r}A[i^x] が計算可能
// https://codeforces.com/contest/1401/problem/F
X Xor_prod(int l, int r, int xor_val) {
assert(Monoid::commute);
X x = Monoid::unit();
FOR(k, log + 1) {
if (l >= r) break;
if (l & 1) { x = Monoid::op(x, dat[(size >> k) + ((l++) ^ xor_val)]); }
if (r & 1) { x = Monoid::op(x, dat[(size >> k) + ((--r) ^ xor_val)]); }
l /= 2, r /= 2, xor_val /= 2;
}
return x;
}
void debug() { print("segtree", dat); }
};
#line 2 "/home/maspy/compro/library/alg/monoid_reverse.hpp"
template <class Monoid>
struct Monoid_Reverse {
using value_type = typename Monoid::value_type;
using X = value_type;
static constexpr X op(const X &x, const X &y) { return Monoid::op(y, x); }
static constexpr X unit() { return Monoid::unit(); }
static const bool commute = Monoid::commute;
};
#line 5 "/home/maspy/compro/library/graph/treemonoid.hpp"
template <typename HLD, typename Monoid, bool edge = false>
struct TreeMonoid {
using RevMonoid = Monoid_Reverse<Monoid>;
using X = typename Monoid::value_type;
HLD &hld;
int N;
SegTree<Monoid> seg;
SegTree<RevMonoid> seg_r;
TreeMonoid(HLD &hld) : hld(hld), N(hld.N), seg(hld.N) {
if (!Monoid::commute) seg_r = SegTree<RevMonoid>(hld.N);
}
TreeMonoid(HLD &hld, vc<X> &dat) : hld(hld), N(hld.N) {
vc<X> seg_raw(N, Monoid::unit());
if (!edge) {
FOR(v, N) seg_raw[hld.LID[v]] = dat[v];
} else {
FOR(e, N - 1) {
int v = hld.e_to_v(e);
seg_raw[hld.LID[v]] = dat[e];
}
}
seg = SegTree<Monoid>(seg_raw);
if (!Monoid::commute) seg_r = SegTree<RevMonoid>(seg_raw);
}
void set(int i, X x) {
if (edge) i = hld.e_to_v(i);
i = hld.LID[i];
seg.set(i, x);
if (!Monoid::commute) seg_r.set(i, x);
}
X prod_path(int u, int v) {
auto pd = hld.get_path_decomposition(u, v, edge);
X val = Monoid::unit();
for (auto &&[a, b]: pd) {
X x = (a <= b ? seg.prod(a, b + 1)
: (Monoid::commute ? seg.prod(b, a + 1)
: seg_r.prod(b, a + 1)));
val = Monoid::op(val, x);
}
return val;
}
// uv path 上で prod_path(u, x) が check を満たす最後の x
// なければ -1
// https://codeforces.com/contest/1059/problem/E
template <class F>
int max_path(F &check, int u, int v) {
if (!check(prod_path(u, u))) return -1;
auto pd = hld.get_path_decomposition(u, v, edge);
X val = Monoid::unit();
for (auto &&[a, b]: pd) {
X x = (a <= b ? seg.prod(a, b + 1)
: (Monoid::commute ? seg.prod(b, a + 1)
: seg_r.prod(b, a + 1)));
if (check(Monoid::op(val, x))) {
val = Monoid::op(val, x);
u = (hld.V[b]);
continue;
}
auto check_tmp = [&](X x) -> bool { return check(Monoid::op(val, x)); };
if (a <= b) {
auto i = seg.max_right(check_tmp, a);
return (i == a ? u : hld.V[i - 1]);
} else {
auto i = (Monoid::commute ? seg.min_left(check_tmp, a + 1)
: seg_r.min_left(check_tmp, a + 1));
return (i == a + 1 ? u : hld.V[i]);
}
}
return v;
}
X prod_subtree(int u) {
int l = hld.LID[u], r = hld.RID[u];
return seg.prod(l + edge, r);
}
void debug() {
print("tree_monoid");
hld.debug();
seg.debug();
seg_r.debug();
}
void doc() {
print("HL分解 + セグ木。");
print("部分木クエリ O(logN) 時間、パスクエリ O(log^2N) 時間。");
}
};
#line 2 "/home/maspy/compro/library/ds/lazysegtree.hpp"
template <typename Lazy>
struct LazySegTree {
using Monoid_X = typename Lazy::X_structure;
using Monoid_A = typename Lazy::A_structure;
using X = typename Monoid_X::value_type;
using A = typename Monoid_A::value_type;
int n, log, size;
vc<X> dat;
vc<A> laz;
LazySegTree() : LazySegTree(0) {}
LazySegTree(int n) : LazySegTree(vc<X>(n, Monoid_X::unit())) {}
LazySegTree(vc<X> v) : n(len(v)) {
log = 1;
while ((1 << log) < n) ++log;
size = 1 << log;
dat.assign(size << 1, Monoid_X::unit());
laz.assign(size, Monoid_A::unit());
FOR(i, n) dat[size + i] = v[i];
FOR3_R(i, 1, size) update(i);
}
void reset() {
fill(all(dat), Monoid_X::unit());
fill(all(laz), Monoid_A::unit());
}
void reset(const vc<X>& v) {
assert(len(v) == n);
reset();
FOR(i, n) dat[size + i] = v[i];
FOR3_R(i, 1, size) update(i);
}
void update(int k) { dat[k] = Monoid_X::op(dat[2 * k], dat[2 * k + 1]); }
void all_apply(int k, A a) {
dat[k] = Lazy::act(dat[k], a);
if (k < size) laz[k] = Monoid_A::op(laz[k], a);
}
void push(int k) {
all_apply(2 * k, laz[k]);
all_apply(2 * k + 1, laz[k]);
laz[k] = Monoid_A::unit();
}
void set(int p, X x) {
assert(0 <= p && p < n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
dat[p] = x;
for (int i = 1; i <= log; i++) update(p >> i);
}
X get(int p) {
assert(0 <= p && p < n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
return dat[p];
}
vc<X> get_all() {
FOR(i, size) push(i);
return {dat.begin() + size, dat.begin() + size + n};
}
X prod(int l, int r) {
assert(0 <= l && l <= r && r <= n);
if (l == r) return Monoid_X::unit();
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
X xl = Monoid_X::unit(), xr = Monoid_X::unit();
while (l < r) {
if (l & 1) xl = Monoid_X::op(xl, dat[l++]);
if (r & 1) xr = Monoid_X::op(dat[--r], xr);
l >>= 1;
r >>= 1;
}
return Monoid_X::op(xl, xr);
}
X prod_all() { return dat[1]; }
void apply(int p, A a) {
assert(0 <= p && p < n);
p += size;
dat[p] = Lazy::act(dat[p], a);
for (int i = 1; i <= log; i++) update(p >> i);
}
void apply(int l, int r, A a) {
assert(0 <= l && l <= r && r <= n);
if (l == r) return;
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
{
int l2 = l, r2 = r;
while (l < r) {
if (l & 1) all_apply(l++, a);
if (r & 1) all_apply(--r, a);
l >>= 1;
r >>= 1;
}
l = l2;
r = r2;
}
for (int i = 1; i <= log; i++) {
if (((l >> i) << i) != l) update(l >> i);
if (((r >> i) << i) != r) update((r - 1) >> i);
}
}
template <typename C>
int max_right(C& check, int l) {
assert(0 <= l && l <= n);
assert(check(Monoid_X::unit()));
if (l == n) return n;
l += size;
for (int i = log; i >= 1; i--) push(l >> i);
X sm = Monoid_X::unit();
do {
while (l % 2 == 0) l >>= 1;
if (!check(Monoid_X::op(sm, dat[l]))) {
while (l < size) {
push(l);
l = (2 * l);
if (check(Monoid_X::op(sm, dat[l]))) {
sm = Monoid_X::op(sm, dat[l]);
l++;
}
}
return l - size;
}
sm = Monoid_X::op(sm, dat[l]);
l++;
} while ((l & -l) != l);
return n;
}
template <typename C>
int min_left(C& check, int r) {
assert(0 <= r && r <= n);
assert(check(Monoid_X::unit()));
if (r == 0) return 0;
r += size;
for (int i = log; i >= 1; i--) push((r - 1) >> i);
X sm = Monoid_X::unit();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!check(Monoid_X::op(dat[r], sm))) {
while (r < size) {
push(r);
r = (2 * r + 1);
if (check(Monoid_X::op(dat[r], sm))) {
sm = Monoid_X::op(dat[r], sm);
r--;
}
}
return r + 1 - size;
}
sm = Monoid_X::op(dat[r], sm);
} while ((r & -r) != r);
return 0;
}
void debug() { print("lazysegtree getall:", get_all()); }
};
#line 2 "/home/maspy/compro/library/ds/dualsegtree.hpp"
template <typename Monoid>
struct DualSegTree {
using A = typename Monoid::value_type;
int n, log, size;
vc<A> laz;
DualSegTree() : DualSegTree(0) {}
DualSegTree(int n) : n(n) {
log = 1;
while ((1 << log) < n) ++log;
size = 1 << log;
laz.assign(size << 1, Monoid::unit());
}
void all_apply(int k, A a) { laz[k] = Monoid::op(laz[k], a); }
void push(int k) {
all_apply(2 * k, laz[k]);
all_apply(2 * k + 1, laz[k]);
laz[k] = Monoid::unit();
}
A get(int p) {
assert(0 <= p && p < n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
return laz[p];
}
vc<A> get_all() {
FOR(i, size) push(i);
return {laz.begin() + size, laz.begin() + size + n};
}
void apply(int l, int r, A a) {
assert(0 <= l && l <= r && r <= n);
if (l == r) return;
l += size;
r += size;
if (!Monoid::commute) {
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
}
{
int l2 = l, r2 = r;
while (l < r) {
if (l & 1) all_apply(l++, a);
if (r & 1) all_apply(--r, a);
l >>= 1;
r >>= 1;
}
l = l2;
r = r2;
}
}
void debug() { print("dualsegtree getall:", get_all()); }
};
#line 4 "/home/maspy/compro/library/graph/dualtreemonoid.hpp"
template <typename HLD, typename Monoid, bool edge = false>
struct DualTreeMonoid {
using X = typename Monoid::value_type;
HLD &hld;
int N;
DualSegTree<Monoid> seg;
DualTreeMonoid(HLD &hld) : hld(hld), N(hld.N), seg(hld.N) {}
X get(int i) {
int v = i;
if (edge) {
auto &&e = hld.G.edges[i];
v = (hld.parent[e.frm] == e.to ? e.frm : e.to);
}
return seg.get(hld.LID[v]);
}
vc<X> get_all() {
vc<X> tmp = seg.get_all();
vc<X> res;
FOR(i, N) {
if (edge && i == N - 1) break;
int v = i;
if (edge) {
auto &&e = hld.G.edges[i];
v = (hld.parent[e.frm] == e.to ? e.frm : e.to);
}
res.eb(tmp[hld.LID[i]]);
}
return res;
}
void apply_path(int u, int v, X x) {
auto pd = hld.get_path_decomposition(u, v, edge);
for (auto &&[a, b]: pd) {
(a <= b ? seg.apply(a, b + 1, x) : seg.apply(b, a + 1, x));
}
return;
}
void apply_subtree(int u, X x) {
int l = hld.LID[u], r = hld.RID[u];
return seg.apply(l + edge, r, x);
}
};
#line 2 "/home/maspy/compro/library/alg/monoid_min.hpp"
template <class X, X INF>
struct Monoid_Min {
using value_type = X;
static constexpr X op(const X &x, const X &y) noexcept { return min(x, y); }
static constexpr X unit() { return INF; }
static constexpr bool commute = true;
};
#line 2 "/home/maspy/compro/library/alg/monoid_max.hpp"
template <class X, X INF>
struct Monoid_Max {
using value_type = X;
static constexpr X op(const X &x, const X &y) noexcept { return max(x, y); }
static constexpr X unit() { return -INF; }
static constexpr bool commute = true;
};
#line 8 "/home/maspy/compro/library/graph/minimum_spanning_tree.hpp"
// return : {T mst_cost, vc<bool> in_mst, Graph MST}
template <typename T>
tuple<T, vc<bool>, Graph<T>> minimum_spanning_tree(Graph<T>& G) {
int N = G.N;
int M = len(G.edges);
vc<pair<T, int>> edges;
FOR(i, M) {
auto& e = G.edges[i];
edges.eb(e.cost, i);
}
sort(all(edges));
vc<bool> in_mst(M);
UnionFind uf(N);
T mst_cost = T(0);
Graph<T> MST(N);
for (auto&& [cost, i]: edges) {
auto& e = G.edges[i];
if (uf.merge(e.frm, e.to)) {
in_mst[i] = 1;
mst_cost += e.cost;
}
}
FOR(i, M) if (in_mst[i]) {
auto& e = G.edges[i];
MST.add(e.frm, e.to, e.cost);
}
MST.build();
return {mst_cost, in_mst, MST};
}
// https://codeforces.com/contest/828/problem/F
// return : {T mst_cost, vc<bool> in_mst, Graph MST, vc<T> dat}
// dat : 辺ごとに、他の辺を保ったときに MST 辺になる最大重み
template <typename T, T INF = (1LL << 60)>
tuple<T, vc<bool>, Graph<T>, vc<T>> minimum_spanning_tree_cycle_data(
Graph<T>& G) {
int N = G.N;
int M = len(G.edges);
auto [mst_cost, in_mst, MST] = minimum_spanning_tree(G);
HLD hld(MST);
vc<T> dat;
FOR(i, M) if (in_mst[i]) dat.eb(G.edges[i].cost);
TreeMonoid<decltype(hld), Monoid_Max<T, INF>, 1> TM1(hld, dat);
DualTreeMonoid<decltype(hld), Monoid_Min<T, INF>, 1> TM2(hld);
FOR(i, M) {
if (!in_mst[i]) {
auto& e = G.edges[i];
TM2.apply_path(e.frm, e.to, e.cost);
}
}
vc<T> ANS(M);
int m = 0;
FOR(i, M) {
auto& e = G.edges[i];
if (in_mst[i])
ANS[i] = TM2.get(m++);
else
ANS[i] = TM1.prod_path(e.frm, e.to);
}
return {mst_cost, in_mst, MST, ANS};
}
#line 7 "main.cpp"
using mint = modint107;
void solve() {
LL(N, M, X);
Graph<ll> G(N);
G.read_graph(M, 1);
auto [c, use, MST] = minimum_spanning_tree(G);
HLD hld(MST);
mint ANS = 0;
for (auto&& e: MST.edges) {
if (hld.parent[e.frm] == e.to) swap(e.frm, e.to);
ll a = hld.subtree_size(e.to);
ll b = N - a;
ANS += mint(a * b) * mint(X).pow(e.cost);
}
print(ANS);
}
signed main() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << setprecision(15);
ll T = 1;
// LL(T);
FOR(T) solve();
return 0;
}