#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
refs:
edi
https://codeforces.com/blog/entry/65042?#comment-491880
*/
const int MOD = 1e9 + 7;
const int N = 2e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
vector<ll> adj[N];
vector<ll> a(N);
pll diam = {-1,-1};
void dfs1(ll u, ll p, ll d){
pll px = {d,u};
amax(diam,px);
trav(v,adj[u]){
if(v == p) conts;
dfs1(v,u,d+1);
}
}
ll dis[N][2];
ll deepest[N][2];
void dfs2(ll u, ll p, ll t){
trav(v,adj[u]){
if(v == p) conts;
dis[v][t] = dis[u][t]+1;
dfs2(v,u,t);
amax(deepest[u][t],deepest[v][t]+1);
}
}
vector<ll> ans(N);
vector<ll> mx_without(N);
vector<ll> first_occ(N,inf2);
vector<pll> active(N);
ll siz = 0;
void dfs3(ll u, ll p, ll d, ll t){
// debug(u);
// debug(siz);
// rep(i,siz){
// debug(active[i]);
// }
// debug(first_occ[2]);
// cout << endl;
ll mx = deepest[u][t];
ll cnt = upper_bound(active.begin(),active.begin()+siz,make_pair(d-mx,-1ll))-active.begin();
if(dis[u][t] >= dis[u][t^1]){
ans[u] = cnt;
}
mx = 0;
trav(v,adj[u]){
if(v == p) conts;
mx_without[v] = mx;
amax(mx,deepest[v][t]+1);
}
mx = 0;
reverse(all(adj[u]));
trav(v,adj[u]){
if(v == p) conts;
amax(mx_without[v],mx);
amax(mx,deepest[v][t]+1);
}
reverse(all(adj[u]));
trav(v,adj[u]){
if(v == p) conts;
vector<array<ll,4>> history;
mx = mx_without[v];
ll new_siz = upper_bound(active.begin(),active.begin()+siz,make_pair(d-mx,-1ll))-active.begin();
ll old_siz = siz;
history.pb({3,siz,-1,-1});
siz = new_siz;
ll x = a[u];
if(first_occ[x] >= siz){
history.pb({1,siz,active[siz].ff,active[siz].ss});
history.pb({2,x,first_occ[x],-1});
history.pb({3,siz,-1,-1});
ll w = active[siz].ss;
if(first_occ[a[w]] == siz){
history.pb({2,a[w],first_occ[a[w]],-1});
first_occ[a[w]] = inf2;
}
active[siz] = {d,u};
first_occ[x] = siz;
siz++;
}
dfs3(v,u,d+1,t);
reverse(all(history));
trav(ar,history){
auto [t,ind,val1,val2] = ar;
if(t == 1){
active[ind] = {val1,val2};
}
else if(t == 2){
first_occ[ind] = val1;
}
else{
siz = ind;
}
}
}
}
void solve(int test_case)
{
ll n,m; cin >> n >> m;
rep1(i,n-1){
ll u,v; cin >> u >> v;
adj[u].pb(v), adj[v].pb(u);
}
rep1(i,n) cin >> a[i];
dfs1(1,-1,0);
ll s = diam.ss;
diam = {-1,-1};
dfs1(s,-1,0);
ll t = diam.ss;
dfs2(s,-1,0);
dfs2(t,-1,1);
dfs3(s,-1,0,0);
dfs3(t,-1,0,1);
rep1(i,n){
cout << ans[i] << endl;
}
}
int main()
{
fastio;
int t = 1;
// cin >> t;
rep1(i, t) {
solve(i);
}
return 0;
}
