#include <bits/stdc++.h>
#ifndef LOCAL
#include "highway.h"
#endif
using namespace std;
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define all(a) (a).begin(), (a).end()
#define Time (clock() * 1.0 / CLOCKS_PER_SEC)
using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
using ld = long double;
template<typename T1, typename T2> bool chkmin(T1& x, T2 y) {
return y < x ? (x = y, true) : false;
}
template<typename T1, typename T2> bool chkmax(T1& x, T2 y) {
return y > x ? (x = y, true) : false;
}
void debug_out() {
cerr << endl;
}
template<typename T1, typename... T2> void debug_out(T1 A, T2... B) {
cerr << ' ' << A;
debug_out(B...);
}
template<typename T> void mdebug_out(T* a, int n) {
for (int i = 0; i < n; ++i)
cerr << a[i] << ' ';
cerr << endl;
}
#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define mdebug(a, n) cerr << #a << ": ", mdebug_out(a, n)
#else
#define debug(...) 1337
#define mdebug(a, n) 1337
#endif
template<typename T> ostream& operator << (ostream& stream, const vector<T>& v) {
for (auto& x : v)
stream << x << ' ';
return stream;
}
template<typename T1, typename T2> ostream& operator << (ostream& stream, const pair<T1, T2>& p) {
return stream << p.first << ' ' << p.second;
}
const int INF32 = 0x3f3f3f3f;
const int maxN = 9e4 + 4;
vector<pii> G[maxN];
int col[maxN];
ll ask(const vector<int>& w);
void answer(int s, int t);
void find_pair(int n, vector<int> eu, vector<int> ev, int A, int B) {
#ifdef LOCAL
#define seed 228
#else
#define seed time(0)
#endif
mt19937 rng(time(0));
uniform_real_distribution<double> dstrb(0.35, 0.51);
const int MIN_RAND_SEP = 100;
int m = eu.size();
for (int v = 0; v < n; ++v)
G[v].clear();
for (int i = 0; i < m; ++i) {
G[eu[i]].emplace_back(ev[i], i);
G[ev[i]].emplace_back(eu[i], i);
}
for (int v = 0; v < n; ++v)
shuffle(all(G[v]), rng);
ll d0 = ask(vector<int>(m, 0));
auto askCol = [&]() -> ll {
vector<int> w(m, 0);
for (int i = 0; i < m; ++i)
if (!col[eu[i]] || !col[ev[i]])
w[i] = 1;
return ask(w);
};
vector<int> ordv(n);
iota(all(ordv), 0);
shuffle(all(ordv), rng);
int vl = -1, vr = n - 1;
while (vr - vl > 1) {
int vm;
if (vr - vl > MIN_RAND_SEP) {
vm = vl + (vr - vl) * dstrb(rng) + 0.5;
} else {
vm = (vl + vr) / 2;
}
for (int i = 0; i <= vm; ++i)
col[ordv[i]] = 0;
for (int i = vm + 1; i < n; ++i)
col[ordv[i]] = 1;
if (askCol() == d0)
vl = vm;
else
vr = vm;
}
int v0 = ordv[vr];
static int qu[maxN], qt, dist[maxN], parv[maxN], pare[maxN];
qu[0] = v0;
fill(dist, dist + n, INF32);
dist[v0] = 0;
qt = 1;
for (int qi = 0; qi < qt; ++qi) {
int u = qu[qi];
for (pii e : G[u]) {
int v = e.fi, eidx = e.se;
if (chkmin(dist[v], dist[u] + 1)) {
pare[v] = eidx;
parv[v] = u;
qu[qt++] = v;
}
}
}
for (int i = 0; i < n; ) {
int j = i;
while (j < n && dist[qu[j]] == dist[qu[i]])
++j;
shuffle(qu + i, qu + j, rng);
i = j;
}
// mdebug(qu, n);
vl = -1, vr = n - 1;
while (vr - vl > 1) {
int vm;
if (vr - vl > MIN_RAND_SEP) {
vm = vl + (vr - vl) * dstrb(rng) + 0.5;
} else {
vm = (vl + vr) / 2;
}
for (int i = 0; i <= vm; ++i)
col[qu[i]] = 1;
for (int i = vm + 1; i < n; ++i)
col[qu[i]] = 0;
if (askCol() == d0)
vr = vm;
else
vl = vm;
}
assert(vl >= 0);
int T = qu[vr];
// debug(vl, vr, T);
vl = -1;
--vr;
while (vr - vl > 1) {
int vm;
if (vr - vl > MIN_RAND_SEP) {
vm = vl + (vr - vl) * dstrb(rng) + 0.5;
} else {
vm = (vl + vr) / 2;
}
for (int i = 0; i <= vm; ++i)
col[qu[i]] = 1;
for (int i = vm + 1; i < n; ++i)
col[qu[i]] = 0;
vector<int> w(m, 0);
for (int i = 0; i < m; ++i)
if (!col[eu[i]] || !col[ev[i]])
w[i] = 1;
for (int v = T; v != v0; v = parv[v]) {
w[pare[v]] = 0;
}
if (ask(w) == d0)
vr = vm;
else
vl = vm;
}
int S = qu[vr];
// debug(S, T);
answer(S, T);
}
#ifdef LOCAL
namespace {
constexpr int MAX_NUM_CALLS = 100;
constexpr long long INF = 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);
cout << N << ' ' << M << ' ' << A << ' ' << B << ' ' << S << ' ' << T << endl;
for (int i = 0; i < M; ++i)
cout << U[i] << ' ' << V[i] << endl;
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, INF);
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() {
freopen("in", "r", stdin);
mt19937 rng(1337);
for (int test = 1; ; ++test) {
N = 3;//9e4;
M = N - 1;//13e4;//N - 1;
A = 1;
B = 1e9;
S = rng() % N;
T = rng() % N;
while (T == S) T = rng() % N;
U.resize(M);
V.resize(M);
graph.assign(N, std::vector<std::pair<int, int>>());
for (int v = 1; v < N; ++v) {
int i = v - 1;
int p = rng() % v;
U[i] = p;
V[i] = v;
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);
if (num_calls > 50) exit(0);
if (test % 10000 == 0) debug(test);
}/**/
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;
}
// int32_t main() {
// #ifdef LOCAL
// freopen("in", "r", stdin);
// #endif
// ios::sync_with_stdio(0);
// cin.tie(0);
// return 0;
// }
#endif
