#include<bits/stdc++.h>
#define ll long long
const int nmax = 2e5 + 5, N = 4e5;
const ll oo = 1e9;
const int lg = 18, M = 4e3;
const int base = 2e5, mod = 1e9 + 7;
#define pii pair<int, int>
#define fi first
#define se second
#define endl "\n"
#define debug(a, n) for(int i = 1; i <= n; ++i) cout << a[i] << ' ';cout << endl
using namespace std;
int n, m;
vector<int> adj[nmax];
int h[nmax], a[nmax], dep[nmax][2], H[nmax];
void dfs_1(int u, int p){
for(auto v : adj[u]){
if(v == p) continue;
H[v] = H[u] + 1;
dfs_1(v, u);
}
}
void ckmax(int &a, int b){
a = max(a, b);
}
vector<int> gg[nmax];
int sz[nmax], up[nmax][lg + 1], mx[nmax];
int nchain = 1, Time = 0, head[nmax], ind[nmax], pos[nmax];
void dfs_4(int u, int p, int id){
sz[u] = 1;
for(auto v : adj[u]){
if(v == p) continue;
dep[v][id] = dep[u][id] + 1;
dfs_4(v, u, id);
sz[u] += sz[v];
}
}
int two[nmax];
void dfs_2(int u, int p){
if(!head[nchain])head[nchain] = u;
ind[u] = nchain;
pos[u] = ++Time;
two[Time] = u;
int idx = -1;
for(auto v : adj[u]){
if(v == p) continue;
up[v][0] = u;
for(int j = 1; j <= lg; ++j) up[v][j] = up[up[v][j - 1]][j - 1];
if(idx == -1 || sz[v] > sz[idx]){
idx = v;
}
}
if(idx != -1){
int v = idx;
dfs_2(v, u);
h[u] = max(h[u], h[v] + 1);
}
for(auto v : adj[u]){
if(v == p || v == idx) continue;
++nchain;
dfs_2(v, u);
h[u] = max(h[u], h[v] + 1);
}
int ma = 0;
for(auto v : adj[u]){
if(v == p) continue;
mx[v] = max(mx[v], ma);
ma = max(ma, h[v] + 1);
}
reverse(adj[u].begin(), adj[u].end());
ma = 0;
for(auto v : adj[u]){
if(v == p) continue;
mx[v] = max(mx[v], ma);
ma = max(ma, h[v] + 1);
}
sort(adj[u].begin(), adj[u].end(),[](int a, int b){
return mx[a] > mx[b];
});
}
int tree[nmax << 2], lz[nmax << 2];
void build(int id, int l, int r){
tree[id] = lz[id] = 0;
if(l == r){
return;
}
int mid = r + l >> 1;
build(id << 1, l, mid);
build(id << 1 | 1, mid + 1, r);
}
void fix(int id, int val){
tree[id] += val;
lz[id] += val;
}
void down(int id){
fix(id << 1,lz[id]);
fix(id << 1 | 1, lz[id]);
lz[id] = 0;
}
void Update(int id, int l, int r, int u, int v, int val){
if(l > v || r < u) return;
if(l >= u && r <= v){
return fix(id, val);
}
down(id);
int mid = r + l >> 1;
Update(id << 1, l, mid, u, v, val);
Update(id << 1 | 1, mid + 1, r, u, v, val);
tree[id] = max(tree[id << 1], tree[id << 1 | 1]);
}
#define Update(u, v, ma) Update(1, 1, n, u, v, ma)
int Get(int id, int l, int r, int u){
if(l == r) return tree[id];
down(id);
int mid = r + l >> 1;
if(u <= mid) return Get(id << 1, l, mid, u);
return Get(id << 1 | 1, mid + 1, r, u);
}
#define Get(u) Get(1, 1, n, u)
int siz = 0;
vector<pii> active(nmax);
int get(int x){
if(x < 0) return 0;
int l = 1, r = siz, kq = siz;
while(l <= r){
int mid = r + l >> 1;
if(active[mid].fi > x){
kq = mid - 1;
r = mid - 1;
}
else l = mid + 1;
}
return kq;
}
struct node{
int id, x, y, z;
};
int first_scc[nmax], ans[nmax][2];
void update(int u, int a,int id, int val){
if(dep[u][id] < dep[a][id] || dep[a][id] == -1) return;
// cerr << dep[u][id] << "#" << dep[a][id] << ' ';
int uchain = ind[u], achain = ind[a];
// cout << u << ' ' << a << ' ' << val << endl;
while(1){
// cerr << u << ' ' << a << endl;
if(achain == uchain){
Update(pos[a], pos[u], val);
// cout << tree[1] << endl;
return;
}
Update(pos[head[uchain]], pos[u], val);
u = up[head[uchain]][0];
uchain = ind[u];
}
// cout << endl;
}
/*
5 4
1 2
2 3
3 4
3 5
1 2 1 2 4
*/
bool check(int u){
if(u == 0 || Get(pos[u]) < 0) return 1;
return 0;
}
int fly(int u, int k){
for(int j = 0; j <= lg; ++j){
if(k >> j & 1){
u = up[u][j];
}
}
return u;
}
void dfs_3(int u, int p, int id){
bool ok = 1;
int idx = -1;
for(auto v : adj[u]){
if(v == p) continue;
if(ok){
int x = min(dep[u][id], mx[v]);
int y = u;
update(up[u][0], fly(u, x), id, -1);
ok = 0;
}
else{
// if()
update(fly(u, mx[v] + 1), fly(u, idx), id, 1);
// if(v == 1) cout << F.get(2) << endl;
}
idx = min(mx[v], dep[u][id]);
vector<node> tmp;
int new_siz = get(max(-1, dep[u][id] - mx[v] - 1));
int x = a[u];
tmp.push_back({2, siz});
siz = new_siz;
// if(v == 1)
// cout << v << ' ' << tree[1] << endl;
if(check(first_scc[x])){
tmp.push_back({1, x, first_scc[x]});
tmp.push_back({3, ++siz, active[siz].fi, active[siz].se});
active[siz] = {dep[u][id], x};
first_scc[x] = u;
}
// cout << v<<"#" << ' ' << siz<< endl;
// for(int i = 1; i <= siz; ++i){
// cout << active[i].fi << ' ' << active[i].se << ' ' << first_scc[active[i].se]<<endl;
// }
// cout << "#" << endl;
// if(v == 1) exit(0);
ans[v][id] = get(dep[v][id] - h[v] - 1);
// if(v == 4) exit(0);
dfs_3(v, u, id);
for(auto [id, x, y, z] : tmp){
if(id == 1){
first_scc[x] = y;
}
else if(id == 2){
siz = x;
}
else{
active[x] = {y, z};
}
}
}
if(idx != -1){
update(up[u][0], fly(u, idx), id, 1);
}
}
main(){
ios_base::sync_with_stdio(0);
cin.tie(0);cout.tie(0);
// freopen("code.inp", "r", stdin);
// freopen("code.out", "w", stdout);
cin >> n >> m;
for(int i = 1; i < n; ++i){
int u, v;
cin >> u >> v;
adj[u].push_back(v);
adj[v].push_back(u);
}
for(int i = 1; i <= n; ++i) cin >> a[i];
int s, t, ma;
ma = -1;
dfs_1(1, -1);
for(int i = 1; i <= n; ++i){
if(ma < H[i]){
ma = max(ma, H[i]);
s = i;
}
}
ma = -1;
dep[0][0] = dep[0][1] = -1;
dfs_1(s, -1);
for(int i = 1; i <= n; ++i){
if(ma < H[i]){
ma = max(ma, H[i]);
t = i;
}
}
active[0] = {-1, 0};
dfs_4(s, -1, 0);
dfs_2(s, -1);
dfs_3(s, -1, 0);
for(int i = 1; i <= n; ++i){
h[i] = 0, mx[i] = 0;
for(int j = 0; j <= lg; ++j) up[i][j] = 0;
head[i] = 0;
}
build(1, 1, n);
nchain = 1;Time = 0;
dfs_4(t, -1, 1);
dfs_2(t, -1);
dfs_3(t, -1, 1);
for(int i = 1; i <= n; ++i) h[i] = 0, mx[i] = 0;
for(int i = 1; i <= n; ++i){
if(dep[i][0] >= dep[i][1]) cout << ans[i][0];
else cout << ans[i][1];
cout << endl;
}
}
/*
*/
