// Hallelujah, praise the one who set me free
// Hallelujah, death has lost its grip on me
// You have broken every chain, There's salvation in your name
// Jesus Christ, my living hope
#include <bits/stdc++.h>
#include "Aoi.h"
using namespace std;
#define REP(i, s, e) for (int i = (s); i < (e); i++)
#define RREP(i, s, e) for (int i = (s); i >= (e); i--)
template <class T>
inline bool mnto(T& a, T b) {return a > b ? a = b, 1 : 0;}
template <class T>
inline bool mxto(T& a, T b) {return a < b ? a = b, 1: 0;}
typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
#define FI first
#define SE second
typedef pair<int, int> ii;
typedef pair<ll, ll> pll;
typedef tuple<int, int, int> iii;
#define ALL(_a) _a.begin(), _a.end()
#define SZ(_a) (int) _a.size()
#define pb push_back
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<ii> vii;
typedef vector<iii> viii;
#ifndef DEBUG
#define cerr if (0) cerr
#endif
const int INF = 1000000005;
const ll LINF = 1000000000000000005ll;
const int MAXN = 10005;
const int MAXM = 20005;
const int MAXK = 305;
const int LOGK = 9;
const int MAXQ = 16;
const int LOGQ = 4;
namespace {
int n, m, q, k;
ll c[MAXM];
vii adj[MAXN];
int subt[MAXN], tid[MAXN], bid[MAXM];
ii p[MAXN];
vii tree[MAXN];
ll d[MAXN];
priority_queue<pll, vector<pll>, greater<pll>> pq;
void dijkstra(int s) {
REP (i, 0, n) {
d[i] = LINF;
}
d[s] = 0;
pq.push({0, s});
while (!pq.empty()) {
auto [ud, u] = pq.top(); pq.pop();
if (ud != d[u]) {
continue;
}
for (auto [v, i] : adj[u]) {
if (mnto(d[v], d[u] + c[i])) {
p[v] = {u, i};
pq.push({d[v], v});
}
}
}
}
void root(int u) {
for (auto [v, i] : tree[u]) {
root(v);
subt[u] += subt[v];
}
}
vi badj[MAXK];
vi bt[MAXK];
vi stk;
void dfs(int u) {
if (tid[u] < q) {
bt[stk.back()].pb(tid[u]);
}
for (auto [v, i] : tree[u]) {
if (!subt[v]) {
continue;
}
if (bid[i] < k) {
badj[stk.back()].pb(bid[i]);
stk.pb(bid[i]);
}
dfs(v);
if (bid[i] < k) {
stk.pop_back();
}
}
}
int bmnt[MAXK];
void broot(int u) {
bmnt[u] = INF;
if (!bt[u].empty()) {
sort(ALL(bt[u]));
bmnt[u] = bt[u][0];
}
for (int v : badj[u]) {
broot(v);
mnto(bmnt[u], bmnt[v]);
}
sort(ALL(badj[u]), [&] (int l, int r) {
return bmnt[l] < bmnt[r];
});
}
int lptr;
int tlabel[MAXQ + 5], blabel[MAXK];
int ids[MAXQ + 5];
int bdfs(int u) {
int ptr = 0;
int nxt = -1;
blabel[u] = lptr;
for (int v : badj[u]) {
while (ptr < SZ(bt[u]) && bt[u][ptr] < bmnt[v]) {
tlabel[nxt] = u;
ids[lptr] = bt[u][ptr];
nxt = bt[u][ptr++];
lptr++;
}
tlabel[nxt] = u;
nxt = bdfs(v);
}
while (ptr < SZ(bt[u])) {
tlabel[nxt] = u;
ids[lptr] = bt[u][ptr];
nxt = bt[u][ptr++];
lptr++;
}
return nxt;
}
vector<int> encode(int b, vector<int> k, vector<vector<int>> a) {
assert(k.size() == a.size());
int n = k.size();
ld bits = 0;
for (int i = 0; i < n; i++) {
bits += a[i].size() * (log(k[i]) / log(b));
}
int m = ceil(bits);
vector<int> x(m);
for (int p = 0; p < m; p++) {
int rem = 0;
for (int i = n - 1; i >= 0; i--) {
for (int j = a[i].size() - 1; j >= 0; j--) {
rem = rem * k[i] + a[i][j];
a[i][j] = rem / b;
rem %= b;
}
}
x[p] = rem;
}
return x;
}
}
string aoi(int N, int M, int Q, int K, vi A, vi B, vll C, vi T, vi X) {
n = N; m = M; q = Q; k = K;
REP (i, 0, m) {
adj[A[i]].pb({B[i], i});
adj[B[i]].pb({A[i], i});
c[i] = C[i];
}
REP (i, 0, n) {
tid[i] = INF;
}
REP (i, 0, q) {
subt[T[i]] = 1;
tid[T[i]] = i;
}
REP (i, 0, m) {
bid[i] = INF;
}
REP (i, 0, k) {
bid[X[i]] = i;
blabel[i] = q;
}
dijkstra(0);
REP (i, 1, n) {
tree[p[i].FI].pb({i, p[i].SE});
}
root(0);
stk.pb(k);
dfs(0);
broot(k);
tlabel[bdfs(k)] = k;
string s;
assert(lptr <= q);
vi tmp = encode(2, vi({q + 1, k + 1, q}), vector<vi>({vi(blabel, blabel + k), vi(tlabel, tlabel + q), vi(ids, ids + q)}));
for (int i : tmp) {
char c = i + '0';
s += c;
}
return s;
}
// Hallelujah, praise the one who set me free
// Hallelujah, death has lost its grip on me
// You have broken every chain, There's salvation in your name
// Jesus Christ, my living hope
#include <bits/stdc++.h>
#include "Bitaro.h"
using namespace std;
#define REP(i, s, e) for (int i = (s); i < (e); i++)
#define RREP(i, s, e) for (int i = (s); i >= (e); i--)
template <class T>
inline bool mnto(T& a, T b) {return a > b ? a = b, 1 : 0;}
template <class T>
inline bool mxto(T& a, T b) {return a < b ? a = b, 1: 0;}
typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
#define FI first
#define SE second
typedef pair<int, int> ii;
typedef pair<ll, ll> pll;
typedef tuple<int, int, int> iii;
#define ALL(_a) _a.begin(), _a.end()
#define SZ(_a) (int) _a.size()
#define pb push_back
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<ii> vii;
typedef vector<iii> viii;
#ifndef DEBUG
#define cerr if (0) cerr
#endif
const int INF = 1000000005;
const ll LINF = 1000000000000000005ll;
const int MAXN = 10005;
const int MAXM = 20005;
const int MAXK = 305;
const int LOGK = 9;
const int MAXQ = 16;
const int LOGQ = 4;
namespace {
int n, m, q, k;
string s;
ll c[MAXM];
vii adj[MAXN];
int ids[MAXQ + 5];
int blabel[MAXK], bid[MAXM];
bool bvis[MAXK];
int bl[MAXK];
int tlabel[MAXQ + 5];
bool tdone[MAXQ + 5];
int qptr;
ii p[MAXN], tp[MAXN];
ll d[MAXN];
priority_queue<pll, vector<pll>, greater<pll>> pq;
vector<vector<int>> decode(int b, vector<int> k, vector<int> l, vector<int> x) {
assert(k.size() == l.size());
int n = k.size(), m = x.size();
vector<vector<int>> a(n);
for (int i = 0; i < n; i++) {
a[i].resize(l[i]);
for (int j = 0; j < l[i]; j++) {
int rem = 0;
for (int p = m - 1; p >= 0; p--) {
rem = rem * b + x[p];
x[p] = rem / k[i];
rem %= k[i];
}
a[i][j] = rem;
}
}
return a;
}
}
void bitaro(int N, int M, int Q, int K, vi A, vi B, vll C, vi T, vi X, string S) {
s = S;
n = N; m = M; q = Q; k = K;
REP (i, 0, m) {
adj[A[i]].pb({B[i], i});
adj[B[i]].pb({A[i], i});
c[i] = C[i];
}
REP (i, 0, k) {
c[X[i]] = -1;
bid[X[i]] = i;
}
vi vs;
for (char c : s) {
vs.pb(c - '0');
}
vector<vi> tmp = decode(2, vi({q + 1, k + 1, q}), vi({k, q, q}), vs);
REP (i, 0, k) {
blabel[i] = tmp[0][i];
}
REP (i, 0, q) {
tlabel[i] = tmp[1][i];
}
REP (i, 0, q) {
ids[i] = tmp[2][i];
}
REP (i, 0, n) {
p[i] = {-1, -1};
}
vi bstk;
bstk.pb(k);
bvis[k] = 1;
REP (l, 0, q) {
int bu = bstk.back();
int u = 0;
if (bu < k) {
u = p[A[X[bu]]].SE == X[bu] ? A[X[bu]] : B[X[bu]];
}
while (!pq.empty()) {
pq.pop();
}
REP (i, 0, n) {
d[i] = LINF;
}
d[u] = 0;
pq.push({0, u});
while (!pq.empty()) {
auto [ud, u] = pq.top(); pq.pop();
if (ud != d[u]) {
continue;
}
for (auto [v, i] : adj[u]) {
if (p[v].FI != -1 && p[v].FI != u) {
continue;
}
if (p[u].FI != -1 && p[u].FI == v) {
continue;
}
ll w = c[i];
if (c[i] == -1) {
if (blabel[bid[i]] != l) {
continue;
}
w = 1;
}
if (mnto(d[v], ud + w)) {
if (c[i] == -1) {
bvis[bid[i]] = 1;
bl[bid[i]] = bl[bstk.back()] + 1;
bstk.pb(bid[i]);
}
tp[v] = {u, i};
pq.push({d[v], v});
}
}
}
int tid = ids[l];
int tu = T[tid];
while (tu != u) {
p[tu] = tp[tu];
tu = tp[tu].FI;
}
while (!bstk.empty() && bstk.back() != tlabel[tid]) {
bvis[bstk.back()] = 0;
bstk.pop_back();
}
assert(!bstk.empty());
}
REP (i, 0, q) {
int u = T[i];
vi e;
while (u) {
e.pb(p[u].SE);
u = p[u].FI;
}
reverse(ALL(e));
answer(e);
}
}
