#include "Aoi.h"
#include <bits/stdc++.h>
using namespace std;
#define int long long
namespace Aoi{
const int N=1e4+10, M=2e4+10;
int n, m;
pair<pair<int, int>, int> edge[M];
vector<int> g[N];
int tr[N], f[N];
void dijkstra(){
memset(f, 0x3f, sizeof f);
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
pq.emplace(f[0]=0, 0);
while (pq.size()){
int u=pq.top().second, d=pq.top().first;
pq.pop();
if (f[u]!=d) continue;
for (int i:g[u]){
int v=edge[i].first.first^edge[i].first.second^u;
int w=edge[i].second;
if (f[v]>d+w) pq.emplace(f[v]=d+w, v), tr[v]=i;
}
}
}
bool used[M];
void trace(int u, vector<int> &ans){
if (u==0) return;
ans.push_back(tr[u]);
return trace(edge[tr[u]].first.first^edge[tr[u]].first.second^u, ans);
}
string solve(int32_t _N, int32_t _M, int32_t Q, int32_t K, vector<int32_t> A,
vector<int32_t> B, vector<long long> C,
vector<int32_t> T, vector<int32_t> X){
n=_N, m=_M;
for (int i=0; i<m; ++i){
edge[i]={{A[i], B[i]}, C[i]};
g[A[i]].push_back(i);
g[B[i]].push_back(i);
}
dijkstra();
string ans;
for (int i:T){
string cur(K, '0');
vector<int> path;
trace(i, path);
for (int j:path) used[j]=1;
for (int j=0; j<K; ++j) cur[j]=used[X[j]]+'0';
for (int j:path) used[j]=0;
ans+=cur;
}
#ifdef sus
ofstream out("spy3.out");
for (int i=0; i<n; ++i) out << f[i] << ' ';
#endif
return ans;
}
}
string aoi(int32_t N, int32_t M, int32_t Q, int32_t K, vector<int32_t> A,
vector<int32_t> B, vector<long long> C,
vector<int32_t> T, vector<int32_t> X) {
return Aoi::solve(N, M, Q, K, A, B, C, T, X);
}
#include "Bitaro.h"
#include <bits/stdc++.h>
using namespace std;
#define int long long
namespace Bitaro{
const int N=1e4+10, M=2e4+10, inf=1e18;
int n, m, q, k;
pair<pair<int, int>, int> edge[M];
vector<int> g[N];
int tr[N];
pair<int, int> f[N];
bool used[M];
void trace(int u, vector<int32_t> &ans){
if (u==0) return;
ans.push_back(tr[u]);
return trace(edge[tr[u]].first.first^edge[tr[u]].first.second^u, ans);
}
vector<int32_t> dijkstra(int t, vector<int> id){
for (int i=0; i<n; ++i) f[i]={inf, inf};
f[0]={0, 0};
priority_queue<pair<pair<int, int>, int>, vector<pair<pair<int, int>, int>>, greater<pair<pair<int, int>, int>>> pq;
pq.emplace(f[0], 0);
set<int> st(id.begin(), id.end());
int cur=0;
while (pq.size()){
auto d=pq.top().first; int u=pq.top().second;
pq.pop();
if (f[u]!=d || d.first!=cur) continue;
if (u==t){
vector<int32_t> ans;
trace(t, ans);
reverse(ans.begin(), ans.end());
return ans;
}
bool check=0;
for (int i:g[u]){
if (check) continue;
if (st.count(i)){
++cur;
int v=edge[i].first.first^edge[i].first.second^u, w=edge[i].second;
pq.emplace(f[v]={cur, d.second}, v);
tr[v]=i;
check=1;
st.erase(i);
}
}
for (int i:g[u]){
if (check || used[i]) continue;
int v=edge[i].first.first^edge[i].first.second^u, w=edge[i].second;
if (f[v].second>d.second+w) pq.emplace(f[v]={d.first, d.second+w}, v), tr[v]=i;
}
}
assert(false);
return {};
}
void solve(int32_t _N, int32_t _M, int32_t Q, int32_t K, vector<int32_t> A, vector<int32_t> B,
vector<long long> C, vector<int32_t> T, vector<int32_t> X,
string s){
n=_N, m=_M, q=Q, k=K;
for (int i:X) used[i]=1;
for (int i=0; i<m; ++i){
edge[i]={{A[i], B[i]}, C[i]};
g[A[i]].push_back(i);
g[B[i]].push_back(i);
}
for (int i=0; i<Q; ++i){
string t=s.substr(i*K, K);
vector<int> id;
for (int j=0; j<K; ++j) if (t[j]=='1') id.push_back(X[j]);
auto ans=dijkstra(T[i], id);
answer(ans);
}
}
}
void bitaro(int32_t N, int32_t M, int32_t Q, int32_t K, vector<int32_t> A, vector<int32_t> B,
vector<long long> C, vector<int32_t> T, vector<int32_t> X,
string s) {
Bitaro::solve(N, M, Q, K, A, B, C, T, X, s);
}
