#include<bits/stdc++.h>
#define int long long
#define pb push_back
#define fast ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
#define MOD 1000000007
#define inf 1000000000000000000
#define fi first
#define se second
#define FOR(i,a,b) for(int i=a;i<=b;i++)
#define FORD(i,a,b) for(int i=a;i>=b;i--)
#define sz(a) ((int)(a).size())
#define endl '\n'
#define pi 3.14159265359
#define TASKNAME "valley"
using namespace std;
template<typename T> bool maximize(T &res, const T &val) { if (res < val){ res = val; return true; }; return false; }
template<typename T> bool minimize(T &res, const T &val) { if (res > val){ res = val; return true; }; return false; }
typedef pair<int,int> ii;
typedef pair<int,ii> iii;
typedef vector<int> vi;
const int MAXN = 3e5 + 9;
iii edge[MAXN];
int n, s, q, e;
vector<int> shops;
vector<ii> queries;
int isShop[MAXN];
vector<int> g[MAXN];
array<int, 4> best[MAXN];
namespace subtask2{
bool check(){
return true;
}
int up[30][MAXN], down[30][MAXN], P[30][MAXN];
int depth[MAXN], dp[MAXN], dist[MAXN], in[MAXN], out[MAXN], timeDfs = 0;
void update(array<int, 4> &res, int x){
FOR(i, 0, 3){
if (x < res[i]){
FORD(j, 3, i + 1){
res[j] = res[j - 1];
}
res[i] = x;
break;
}
}
}
int choose(array<int, 4> &res, vector<int> eliminate){
sort(eliminate.begin(), eliminate.end());
assert(eliminate.size() < 4);
FOR(i, 0, 3){
if (i >= eliminate.size()) return res[i];
if (res[i] != eliminate[i]) return res[i];
}
return 0;
}
inline int getDist(int u, int v){
return abs(dist[v] - dist[u]);
}
void init(){
function<void(int, int)> dfs = [&](int u, int p){
best[u] = {inf, inf, inf, inf};
in[u] = ++timeDfs;
dp[u] = inf;
if (isShop[u]) {
minimize(dp[u], 0LL);
update(best[u], 0LL);
}
for(int id: g[u]){
int v = edge[id].se.fi + edge[id].se.se - u;
int w = edge[id].fi;
if (v == p) continue;
depth[v] = depth[u] + 1;
dist[v] = dist[u] + w;
dfs(v, u);
minimize(dp[u], dp[v] + w);
update(best[u], dp[v] + w);
P[0][v] = u;
}
for(int id: g[u]){
int v = edge[id].se.fi + edge[id].se.se - u;
int w = edge[id].fi;
if (v == p) continue;
up[0][v] = (isShop[v]) ? 0 : choose(best[u], {dp[v] + w}) + w;
down[0][v] = min((isShop[v]) ? (w) : inf, choose(best[u], {dp[v] + w}));
}
out[u] = timeDfs;
};
dfs(1, -1);
P[0][1] = -1; up[0][1] = (isShop[1]) ? 0 : inf; down[0][1] = inf;
// printf("\n");
// FOR(i, 1, n){
// printf("%lld ", down[0][i]);
// }
// printf("\n");
FOR(i, 1, 20){
FOR(j, 1, n){
if (P[i - 1][j] == -1) P[i][j] = -1;
else P[i][j] = P[i - 1][P[i - 1][j]];
up[i][j] = down[i][j] = inf;
if (P[i][j] != -1){
up[i][j] = min(up[i - 1][P[i - 1][j]] + getDist(P[i - 1][j], j),
up[i - 1][j]);
down[i][j] = min(down[i - 1][P[i - 1][j]],
down[i - 1][j] + getDist(P[i - 1][j], P[i][j]));
}
// printf("%lld ", down[i][j]);
}
// printf("\n\n");
}
}
int getPath(int u, int v, bool Up){ //tu u den v va chieu cao can thiet d, Up: 1 trong 2 case.
int cur, res;
if (Up){ //di tu u len v
res = inf;
cur = u;
FORD(i, 20, 0){
if (P[i][cur] != -1 and depth[P[i][cur]] >= depth[v]){
minimize(res, getDist(u, cur) + up[i][cur]);
cur = P[i][cur];
}
}
}
else{ //di xuong tu u xuong v
cur = v;
res = inf;
FORD(i, 20, 0){
if (P[i][cur] != -1 and depth[P[i][cur]] >= depth[u]){
minimize(res, getDist(u, P[i][cur]) + down[i][cur]);
cur = P[i][cur];
}
}
}
return res;
}
int kthJump(int u, int k){
// cerr << u << ' ' << k << endl;
if (k < 0 or k > depth[u]) return -1;
FORD(i, 20, 0){
if (k & (1 << i)) u = P[i][u];
}
return u;
}
int getLCA(int u, int v){
if (depth[u] < depth[v]) swap(u, v);
FORD(i, 20, 0){
if (P[i][u] != -1 and depth[P[i][u]] >= depth[v]) u = P[i][u];
}
if (u == v) return u;
FORD(i, 20, 0){
if (P[i][u] != -1 and P[i][v] != -1 and P[i][u] != P[i][v]) u = P[i][u], v = P[i][v];
}
return P[0][u];
}
inline bool inSubtree(int u, int v){ //u co nam trong cay con goc v hay khong
return in[u] >= in[v] and in[u] <= out[v];
}
void solveQueries(){
FOR(i, 1, q){
int I, R;
I = queries[i - 1].fi;
R = queries[i - 1].se;
int u = edge[I].se.fi;
int v = edge[I].se.se;
int w = edge[I].fi;
if (depth[u] > depth[v]) swap(u, v);
int res = inf;
if ((inSubtree(R, v) ^ inSubtree(e, v)) == 0) {
cout << "escaped\n";
}
else{
if (isShop[R]) res = 0;
if (inSubtree(R, v)){
minimize(res, getPath(R, v, 1));
minimize(res, choose(best[R], {}));
}
else if (inSubtree(R, u)){
int beforeR = kthJump(R, depth[R] - depth[u] - 1);
if (beforeR != -1) minimize(res, getPath(R, beforeR, 1));
if (R != u) minimize(res, choose(best[R], {}));
if (R == u) minimize(res, choose(best[u], {dp[v] + w}));
else minimize(res, choose(best[u], {dp[v] + w, dp[beforeR] + getDist(beforeR, u)}) + getDist(R, u));
minimize(res, getPath(u, 1, 1) + getDist(R, u));
}
else {
int acs = getLCA(u, R);
int beforeR = kthJump(R, depth[R] - depth[acs] - 1);
int beforeU = kthJump(u, depth[u] - depth[acs] - 1);
// printf("%lld %lld\n", R, acs);
if (R == acs){
minimize(res, choose(best[R], {dp[beforeU] + dist[beforeU] - dist[R]}));
minimize(res, getPath(R, u, 0));
minimize(res, choose(best[u], {dp[v] + w}) + getDist(R, u));
minimize(res, getPath(R, 1, 1));
}
else{
minimize(res, getPath(R, beforeR, 1));
minimize(res, choose(best[R], {}));
minimize(res, getDist(R, acs) + choose(best[acs],{dp[beforeU] + getDist(beforeU, acs), dp[beforeR] + getDist(beforeR, acs)}));
minimize(res, getPath(acs, u, 0) + getDist(acs, R));
// printf("%lld %lld %lld %lld\n",res, acs, u, getPath(acs, u, 0));
minimize(res, choose(best[u], {dp[v] + w}) + getDist(acs, R) + getDist(acs, u));
minimize(res, getPath(acs, 1, 1) + getDist(R, acs));
}
}
if (res < inf) cout << res << endl;
else cout << "oo\n";
}
}
}
void solve(){
init();
solveQueries();
}
}
main()
{
fast;
if (fopen(TASKNAME".inp","r")){
freopen(TASKNAME".inp","r",stdin);
freopen(TASKNAME".out","w",stdout);
}
cin >> n >> s >> q >> e;
FOR(i, 1, n - 1){
cin >> edge[i].se.fi >> edge[i].se.se >> edge[i].fi;
g[edge[i].se.fi].pb(i);
g[edge[i].se.se].pb(i);
}
FOR(i, 1, s){
int u;
cin >> u;
shops.pb(u);
isShop[u] = 1;
}
FOR(i, 1, q){
int I, R;
cin >> I >> R;
queries.pb({I, R});
}
if (subtask2::check()) return subtask2::solve(), 0;
}
/**
Warning:
- MLE / TLE?
- Gioi han mang?
- Gia tri max phai luon gan cho -INF
- long long co can thiet khong?
- tran mang.
- code can than hon
- Nho sinh test de tranh RTE / TLE
--> Coi lai truoc khi nop
**/
