This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define int long long
#define FOR(i, a, b) for (int i = (a); i <= (b); i++)
#define FORD(i, a, b) for (int i = (b); i >= (a); i --)
#define REP(i, a) for (int i = 0; i < (a); ++i)
#define REPD(i, a) for (int i = (a) - 1; i >= 0; --i)
#define MASK(i) (1LL << (i))
#define BIT(x, i) (((x) >> (i)) & 1)
constexpr ll LINF = (1ll << 60);
constexpr int INF = (1ll << 30);
constexpr int Mod = 1e9 + 7;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
/*
Phu Trong from Nguyen Tat Thanh High School for gifted student
*/
template <class X, class Y>
bool minimize(X &x, const Y &y){
X eps = 1e-9;
if (x > y + eps) {x = y; return 1;}
return 0;
}
template <class X, class Y>
bool maximize(X &x, const Y &y){
X eps = 1e-9;
if (x + eps < y) {x = y; return 1;}
return 0;
}
int numNode, numEdge;
#define MAX 300005
#define LOG 20
bool in[MAX];
struct Edge{
int u, v;
Edge(){}
Edge(int _u, int _v):u(_u), v(_v){}
int other(int x){
return (x ^ u ^ v);
}
} edge[MAX];
vector<int> G[MAX];
int up[MAX][21], to[MAX], dep[MAX];
void dfs(int u, int p = -1){
for (int&i : G[u]){
int v = edge[i].other(u);
if(v ^ p){
up[v][0] = u;
dep[v] = dep[u] + 1;
to[v] = i;
for (int i = 1; i < LOG; ++i) up[v][i] = up[up[v][i - 1]][i - 1];
dfs(v, u);
}
}
}
int lca(int u, int v){
if (dep[u] > dep[v]) swap(u, v);
int dis = dep[u] - dep[v];
for (int i = 0; MASK(i) <= dis; ++i) if(BIT(dis, i)){
u = up[u][i];
}
if(u == v) return u;
int k = __lg(dep[u]);
for (int i = k; i >= 0; --i) if(up[u][i] != up[v][i]){
u = up[u][i], v = up[v][i];
}
return up[u][0];
}
bool assigned[MAX];
int ans[MAX];
int pa[MAX];
int find(int u){
return u == pa[u] ? u : pa[u] = find(pa[u]);
}
bool joint(int u, int v){
u = find(u), v = find(v);
if(u == v) return false;
pa[v] = u;
return true;
}
void process(void){
cin >> numNode >> numEdge;
for (int i = 1; i <= numEdge; ++i){
cin >> edge[i].u >> edge[i].v;
}
for (int i = 1; i < numNode; ++i){
int id; cin >> id;
G[edge[id].u].emplace_back(id);
G[edge[id].v].emplace_back(id);
in[id] = true;
}
dfs(1);
int label = 0;
for (int i = 1; i <= numNode; ++i) pa[i] = i;
for (int i = 1; i <= numEdge; ++i){
if(assigned[i]) continue;
assigned[i] = true;
if(in[i]){
ans[i] = ++label;
if (dep[edge[i].u] < dep[edge[i].v]) swap(edge[i].u, edge[i].v);
joint(edge[i].v, edge[i].u);
continue;
}
vector<int> target;
int anc = lca(edge[i].u, edge[i].v);
for (int node : {edge[i].u, edge[i].v}){
while(node != anc && dep[find(node)] >= dep[anc]){
node = find(node);
if(node == anc) break;
if (to[node]) target.push_back(to[node]);
joint(up[node][0], node);
node = up[node][0];
}
}
sort(target.begin(), target.end());
for (int &id : target){
ans[id] = ++label;
assigned[id] = true;
}
ans[i] = ++label;
}
for (int i = 1; i <= numEdge; ++i){
cout << ans[i] << " ";
}
}
signed main(){
#define name "Whisper"
cin.tie(nullptr) -> sync_with_stdio(false);
//freopen(name".inp", "r", stdin);
//freopen(name".out", "w", stdout);
process();
return (0 ^ 0);
}
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