#include <bits/stdc++.h>

using namespace std;
using ll = long long;
// #define int ll
using PII = pair<ll, ll>;

#define FOR(i, a, n) for (ll i = (ll)a; i < (ll)n; ++i)
#define REP(i, n) FOR(i, 0, n)
#define ALL(x) x.begin(), x.end()

template<typename T> T &chmin(T &a, const T &b) { return a = min(a, b); }
template<typename T> T &chmax(T &a, const T &b) { return a = max(a, b); }
template<typename T> bool IN(T a, T b, T x) { return a<=x&&x<b; }
template<typename T> T ceil(T a, T b) { return a/b + !!(a%b); }

template<typename T> vector<T> make_v(size_t a) { return vector<T>(a); }
template<typename T,typename... Ts>
auto make_v(size_t a,Ts... ts) {
    return vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...));
}
template<typename T,typename V> typename enable_if<is_class<T>::value==0>::type
fill_v(T &t, const V &v) { t=v; }
template<typename T,typename V> typename enable_if<is_class<T>::value!=0>::type
fill_v(T &t, const V &v ) { for(auto &e:t) fill_v(e,v); }

template<class S,class T>
ostream &operator <<(ostream& out,const pair<S,T>& a) {
    out<<'('<<a.first<<','<<a.second<<')'; return out;
}
template<class T>
ostream &operator <<(ostream& out,const vector<T>& a){
    out<<'[';
    for(const T &i: a) out<<i<<',';
    out<<']';
    return out;
}
template<class T>
ostream &operator <<(ostream& out, const set<T>& a) {
    out<<'{';
    for(const T &i: a) out<<i<<',';
    out<<'}';
    return out;
}
template<class T, class S>
ostream &operator <<(ostream& out, const map<T,S>& a) {
    out<<'{';
    for(auto &i: a) out<<i<<',';
    out<<'}';
    return out;
}

int dx[] = {0, 1, 0, -1}, dy[] = {1, 0, -1, 0}; // DRUL
const int INF = 1<<30;
const ll LLINF = 1LL<<60;
const ll MOD = 1000000007;

struct UnionFind {
    ll ans = 0;
    map<ll,ll> par, s, e;
    int find(int x) {
        if(par.find(x) == par.end()) {
            par[x] = x;
            s[x] = 1;
            e[x] = 0;
        }
        if(par[x] == x) return x;
        return par[x] = find(par[x]);
    }
    void unite(int x, int y) {
        x = find(x);
        y = find(y);
        if(x == y) {
            ans -= min(s[x], e[x]);
            e[x]++;
            ans += min(s[x], e[x]);
        } else if(s[x] < s[y]) {
            ans -= min(s[x], e[x]) + min(s[y], e[y]);
            par[x] = y;
            s[y] = s[x] + s[y];
            e[y] = e[x] + e[y] + 1;
            ans += min(s[y], e[y]);
        } else {
            ans -= min(s[x], e[x]) + min(s[y], e[y]);
            par[y] = x;
            s[x] = s[x] + s[y];
            e[x] = e[x] + e[y] + 1;
            ans += min(s[x], e[x]);
        }
    }
};

struct info {
    UnionFind uf;
    vector<PII> edges;
};

ll n, k, c[100010], d[100010], ans[100010];
vector<ll> g[100010];
void merge(info &a, info &b) {
    if(a.edges.size() < b.edges.size()) swap(a, b);
    for(auto i: b.edges) {
        a.uf.unite(i.first, i.second);
        a.edges.emplace_back(i);
    }
}
info dfs(ll v, ll p) {
    info nret;
    nret.edges.push_back({c[v], d[v]});
    nret.uf.unite(c[v], d[v]);
    for(auto to: g[v]) if(to != p) {
        info ret = dfs(to, v);
        merge(nret, ret);
    }
    ans[v] = nret.uf.ans;
    return nret;
}

signed main(void)
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    cin >> n >> k;
    REP(i, n-1) {
        ll a, b;
        cin >> a >> b;
        a--, b--;
        g[a].push_back(b);
        g[b].push_back(a);
    }
    REP(i, n) cin >> c[i] >> d[i], c[i]--, d[i]--;

    dfs(0, -1);
    REP(i, n) cout << ans[i] << endl;

    return 0;
}



Measured memory_bytes: 78284