This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
// Success consists of going from failure to failure without loss of enthusiasm
#include <bits/stdc++.h>
using namespace std;
#define nl '\n'
#define pb push_back
#define mp make_pair
#define f first
#define s second
#define sz(x) int(x.size())
template<class T> using V = vector<T>;
using vi = V<int>;
using ll = long long;
using pi = pair<int, int>;
using vpi = V<pi>;
using vl = V<ll>;
using db = long double;
const int INF = 1e9 + 10;
struct DSU {
vi e; void init(int N) { e = vi(N, -1); }
int get(int x) { return e[x] < 0 ? x : e[x] = get(e[x]); }
void unite(int x, int y) {
x = get(x), y = get(y);
e[x] += e[y]; e[y] = x;
}
};
int main() {
cin.tie(0)->sync_with_stdio(0);
int N, M; cin >> N >> M;
vpi E;
for(int i = 0; i < M; i++) {
int u, v; cin >> u >> v; --u, --v;
E.pb(mp(u, v));
}
V<vpi> adj(N); vi on(M);
for(int i = 0; i < N - 1; i++) {
int x; cin >> x; --x;
on[x] = 1;
auto [u, v] = E[x];
adj[u].pb(mp(v, x));
adj[v].pb(mp(u, x));
}
vi par(N), id(N), dep(N);
function<void(int)> dfs = [&](int u) {
for(auto& e : adj[u]) if (e.f != par[u]) {
id[e.f] = e.s; dep[e.f] = dep[u] + 1; par[e.f] = u; dfs(e.f);
}
};
par[0] = -1, id[0] = -1, dep[0] = 0; dfs(0);
vi ans(M, -1); int cur = 1; DSU D; D.init(N);
for(int i = 0; i < M; i++) {
auto [u, v] = E[i];
if (on[i]) {
if (dep[u] > dep[v]) swap(u, v);
assert(par[v] == u && id[v] == i);
D.unite(u, v); ans[i] = cur++;
continue;
}
vi upd;
while(1) {
int a = D.get(u), b = D.get(v);
if (a == b) break;
if (dep[a] < dep[b]) swap(a, b);
assert(par[a] != -1);
D.unite(par[a], a);
upd.pb(id[a]);
}
sort(begin(upd), end(upd));
for(auto x : upd) ans[x] = cur++;
ans[i] = cur++;
}
for(auto x : ans) cout << x << " ";
cout << nl;
return 0;
}
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