/*************************************
* author: marvinthang *
* created: 27.06.2023 08:31:11 *
*************************************/
#include "highway.h"
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define left ___left
#define right ___right
#define TIME (1.0 * clock() / CLOCKS_PER_SEC)
#define MASK(i) (1LL << (i))
#define BIT(x, i) ((x) >> (i) & 1)
#define __builtin_popcount __builtin_popcountll
#define ALL(v) (v).begin(), (v).end()
#define REP(i, n) for (int i = 0, _n = (n); i < _n; ++i)
#define REPD(i, n) for (int i = (n); i--; )
#define FOR(i, a, b) for (int i = (a), _b = (b); i < _b; ++i)
#define FORD(i, b, a) for (int i = (b), _a = (a); --i >= _a; )
#define FORE(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i)
#define FORDE(i, b, a) for (int i = (b), _a = (a); i >= _a; --i)
#define scan_op(...) istream & operator >> (istream &in, __VA_ARGS__ &u)
#define print_op(...) ostream & operator << (ostream &out, const __VA_ARGS__ &u)
#ifdef LOCAL
#include "debug.h"
#else
#define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
#define DB(...) 23
#define db(...) 23
#define debug(...) 23
#endif
template <class U, class V> scan_op(pair <U, V>) { return in >> u.first >> u.second; }
template <class T> scan_op(vector <T>) { for (size_t i = 0; i < u.size(); ++i) in >> u[i]; return in; }
template <class U, class V> print_op(pair <U, V>) { return out << '(' << u.first << ", " << u.second << ')'; }
template <size_t i, class T> ostream & print_tuple_utils(ostream &out, const T &tup) { if constexpr(i == tuple_size<T>::value) return out << ")"; else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); }
template <class ...U> print_op(tuple<U...>) { return print_tuple_utils<0, tuple<U...>>(out, u); }
template <class Con, class = decltype(begin(declval<Con>()))> typename enable_if <!is_same<Con, string>::value, ostream&>::type operator << (ostream &out, const Con &con) { out << '{'; for (__typeof(con.begin()) it = con.begin(); it != con.end(); ++it) out << (it == con.begin() ? "" : ", ") << *it; return out << '}'; }
template <class A, class B> bool minimize(A &a, B b) { if (a > b) { a = b; return true; } return false; }
template <class A, class B> bool maximize(A &a, B b) { if (a < b) { a = b; return true; } return false; }
// end of template
const long long INF = 1e18;
void find_pair(int N, vector <int> U, vector <int> V, int A, int B) {
int M = U.size();
int l = 0, r = M - 2;
vector <int> w(M);
long long len = ask(w);
while (l <= r) {
int m = l + r >> 1;
fill(w.begin(), w.begin() + m + 1, 1);
fill(m + 1 + ALL(w), 0);
if (ask(w) > len) r = m - 1;
else l = m + 1;
}
int bl = l;
fill(ALL(w), 1);
int s = U[bl];
vector <vector <int>> adj(N);
FOR(i, bl, M) {
adj[U[i]].push_back(i);
adj[V[i]].push_back(i);
}
vector <int> dist(N, -1), trace(N, -1);
queue <int> q;
q.push(s);
dist[s] = 0;
trace[s] = s;
vector <int> ver;
while (!q.empty()) {
int u = q.front();
ver.push_back(u);
q.pop();
for (int id: adj[u]) {
int v = U[id] ^ V[id] ^ u;
if (!~dist[v]) {
dist[v] = dist[u] + 1;
trace[v] = id;
w[id] = 0;
q.push(v);
}
}
}
l = 1, r = (int) ver.size() - 1;
while (l <= r) {
int m = l + r >> 1;
FOR(i, m, ver.size()) w[trace[ver[i]]] = 1;
if (ask(w) > len) l = m + 1;
else r = m - 1;
FOR(i, m, ver.size()) w[trace[ver[i]]] = 0;
}
int u = ver[r];
int du = dist[u];
vector <int> candidates;
REP(v, N) if (v != u && dist[v] == len / A - du) candidates.push_back(v);
fill(ALL(dist), -1);
dist[u] = 0;
q.push(u);
while (!q.empty()) {
int u = q.front();
ver.push_back(u);
q.pop();
for (int id: adj[u]) {
int v = U[id] ^ V[id] ^ u;
if (v != s && !~dist[v]) {
dist[v] = dist[u] + 1;
q.push(v);
}
}
}
REPD(i, candidates.size()) if (~dist[candidates[i]] && dist[candidates[i]] <= len) {
swap(candidates[i], candidates.back());
candidates.pop_back();
}
l = 0, r = (int) candidates.size() - 2;
while (l <= r) {
int m = l + r >> 1;
REP(i, m + 1) w[trace[candidates[i]]] = 1;
if (ask(w) > len) r = m - 1;
else l = m + 1;
REP(i, m + 1) w[trace[candidates[i]]] = 0;
}
int v = candidates[l];
answer(u, v);
}
#ifdef LOCAL
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <queue>
#include <utility>
#include <vector>
#include "highway.h"
namespace {
constexpr int MAX_NUM_CALLS = 100;
constexpr long long inffff = 1LL << 61;
int N, M, A, B, S, T;
std::vector<int> U, V;
std::vector<std::vector<std::pair<int, int>>> graph;
bool answered, wrong_pair;
int num_calls;
int read_int() {
int x;
if (scanf("%d", &x) != 1) {
fprintf(stderr, "Error while reading input\n");
exit(1);
}
return x;
}
void wrong_answer(const char *MSG) {
printf("Wrong Answer: %s\n", MSG);
exit(0);
}
} // namespace
long long ask(const std::vector<int> &w) {
if (++num_calls > MAX_NUM_CALLS) {
wrong_answer("more than 100 calls to ask");
}
if (w.size() != (size_t)M) {
wrong_answer("w is invalid");
}
for (size_t i = 0; i < w.size(); ++i) {
if (!(w[i] == 0 || w[i] == 1)) {
wrong_answer("w is invalid");
}
}
std::vector<bool> visited(N, false);
std::vector<long long> current_dist(N, inffff);
std::queue<int> qa, qb;
qa.push(S);
current_dist[S] = 0;
while (!qa.empty() || !qb.empty()) {
int v;
if (qb.empty() ||
(!qa.empty() && current_dist[qa.front()] <= current_dist[qb.front()])) {
v = qa.front();
qa.pop();
} else {
v = qb.front();
qb.pop();
}
if (visited[v]) {
continue;
}
visited[v] = true;
long long d = current_dist[v];
if (v == T) {
return d;
}
for (auto e : graph[v]) {
int vv = e.first;
int ei = e.second;
if (!visited[vv]) {
if (w[ei] == 0) {
if (current_dist[vv] > d + A) {
current_dist[vv] = d + A;
qa.push(vv);
}
} else {
if (current_dist[vv] > d + B) {
current_dist[vv] = d + B;
qb.push(vv);
}
}
}
}
}
return -1;
}
void answer(int s, int t) {
if (answered) {
wrong_answer("answered not exactly once");
}
if (!((s == S && t == T) || (s == T && t == S))) {
wrong_pair = true;
}
answered = true;
}
int main() {
file("highway");
N = read_int();
M = read_int();
A = read_int();
B = read_int();
S = read_int();
T = read_int();
U.resize(M);
V.resize(M);
graph.assign(N, std::vector<std::pair<int, int>>());
for (int i = 0; i < M; ++i) {
U[i] = read_int();
V[i] = read_int();
graph[U[i]].push_back({V[i], i});
graph[V[i]].push_back({U[i], i});
}
answered = false;
wrong_pair = false;
num_calls = 0;
find_pair(N, U, V, A, B);
if (!answered) {
wrong_answer("answered not exactly once");
}
if (wrong_pair) {
wrong_answer("{s, t} is wrong");
}
printf("Accepted: %d\n", num_calls);
return 0;
}
#endif
