Bob Equilibrium

#include <bits/stdc++.h>
using namespace std;
 
using ll = long long;
using ld = long double;
using db = double;
using str = string;  // yay python!
 
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<db, db>;
 
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>;
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
 
#define tcT template <class T
#define tcTU tcT, class U
// ^ lol this makes everything look weird but I'll try it
tcT > using V = vector<T>;
tcT, size_t SZ > using AR = array<T, SZ>;
tcT > using PR = pair<T, T>;
 
// pairs
#define mp make_pair
#define f first
#define s second
 
// vectors
// oops size(x), rbegin(x), rend(x) need C++17
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend()
#define sor(x) sort(all(x))
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pb push_back
#define eb emplace_back
#define pf push_front
 
#define lb lower_bound
#define ub upper_bound
tcT > int lwb(V<T> &a, const T &b) { return int(lb(all(a), b) - bg(a)); }
 
// loops
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define F0R(i, a) FOR(i, 0, a)
#define ROF(i, a, b) for (int i = (b) - 1; i >= (a); --i)
#define R0F(i, a) ROF(i, 0, a)
#define trav(a, x) for (auto &a : x)
 
const int MOD = 1e9 + 7;  // 998244353;
const int MX = 2e5 + 5;
const ll INF = 1e18;  // not too close to LLONG_MAX
const ld PI = acos((ld)-1);
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};  // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
 
// bitwise ops
// also see https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html
constexpr int pct(int x) { return __builtin_popcount(x); }  // # of bits set
constexpr int bits(int x) {  // assert(x >= 0); // make C++11 compatible until
	                         // USACO updates ...
	return x == 0 ? 0 : 31 - __builtin_clz(x);
}  // floor(log2(x))
constexpr int p2(int x) { return 1 << x; }
constexpr int msk2(int x) { return p2(x) - 1; }
 
ll cdiv(ll a, ll b) {
	return a / b + ((a ^ b) > 0 && a % b);
}  // divide a by b rounded up
ll fdiv(ll a, ll b) {
	return a / b - ((a ^ b) < 0 && a % b);
}  // divide a by b rounded down
 
tcT > bool ckmin(T &a, const T &b) { return b < a ? a = b, 1 : 0; }  // set a = min(a,b)
tcT > bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }
 
tcTU > T fstTrue(T lo, T hi, U f) {
	hi++;
	assert(lo <= hi);  // assuming f is increasing
	while (lo < hi) {  // find first index such that f is true
		T mid = lo + (hi - lo) / 2;
		f(mid) ? hi = mid : lo = mid + 1;
	}
	return lo;
}
tcTU > T lstTrue(T lo, T hi, U f) {
	lo--;
	assert(lo <= hi);  // assuming f is decreasing
	while (lo < hi) {  // find first index such that f is true
		T mid = lo + (hi - lo + 1) / 2;
		f(mid) ? lo = mid : hi = mid - 1;
	}
	return lo;
}
tcT > void remDup(vector<T> &v) {  // sort and remove duplicates
	sort(all(v));
	v.erase(unique(all(v)), end(v));
}
tcTU > void erase(T &t, const U &u) {  // don't erase
	auto it = t.find(u);
	assert(it != end(t));
	t.erase(it);
}  // element that doesn't exist from (multi)set
 
// INPUT
#define tcTUU tcT, class... U
tcT > void re(complex<T> &c);
tcTU > void re(pair<T, U> &p);
tcT > void re(V<T> &v);
tcT, size_t SZ > void re(AR<T, SZ> &a);
 
tcT > void re(T &x) { cin >> x; }
void re(db &d) {
	str t;
	re(t);
	d = stod(t);
}
void re(ld &d) {
	str t;
	re(t);
	d = stold(t);
}
tcTUU > void re(T &t, U &...u) {
	re(t);
	re(u...);
}
 
tcT > void re(complex<T> &c) {
	T a, b;
	re(a, b);
	c = {a, b};
}
tcTU > void re(pair<T, U> &p) { re(p.f, p.s); }
tcT > void re(V<T> &x) { trav(a, x) re(a); }
tcT, size_t SZ > void re(AR<T, SZ> &x) { trav(a, x) re(a); }
tcT > void rv(int n, V<T> &x) {
	x.rsz(n);
	re(x);
}
 
// TO_STRING
#define ts to_string
str ts(char c) { return str(1, c); }
str ts(const char *s) { return (str)s; }
str ts(str s) { return s; }
str ts(bool b) {
#ifdef LOCAL
	return b ? "true" : "false";
#else
	return ts((int)b);
#endif
}
tcT > str ts(complex<T> c) {
	stringstream ss;
	ss << c;
	return ss.str();
}
str ts(V<bool> v) {
	str res = "{";
	F0R(i, sz(v)) res += char('0' + v[i]);
	res += "}";
	return res;
}
template <size_t SZ> str ts(bitset<SZ> b) {
	str res = "";
	F0R(i, SZ) res += char('0' + b[i]);
	return res;
}
tcTU > str ts(pair<T, U> p);
tcT > str ts(T v) {  // containers with begin(), end()
#ifdef LOCAL
	bool fst = 1;
	str res = "{";
	for (const auto &x : v) {
		if (!fst) res += ", ";
		fst = 0;
		res += ts(x);
	}
	res += "}";
	return res;
#else
	bool fst = 1;
	str res = "";
	for (const auto &x : v) {
		if (!fst) res += " ";
		fst = 0;
		res += ts(x);
	}
	return res;
 
#endif
}
tcTU > str ts(pair<T, U> p) {
#ifdef LOCAL
	return "(" + ts(p.f) + ", " + ts(p.s) + ")";
#else
	return ts(p.f) + " " + ts(p.s);
#endif
}
 
// OUTPUT
tcT > void pr(T x) { cout << ts(x); }
tcTUU > void pr(const T &t, const U &...u) {
	pr(t);
	pr(u...);
}
void ps() { pr("\n"); }  // print w/ spaces
tcTUU > void ps(const T &t, const U &...u) {
	pr(t);
	if (sizeof...(u)) pr(" ");
	ps(u...);
}
 
// DEBUG
void DBG() { cerr << "]" << endl; }
tcTUU > void DBG(const T &t, const U &...u) {
	cerr << ts(t);
	if (sizeof...(u)) cerr << ", ";
	DBG(u...);
}
#ifdef LOCAL  // compile with -DLOCAL, chk -> fake assert
#define dbg(...)                                                                       \
	cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#define chk(...)                                                                       \
	if (!(__VA_ARGS__))                                                                \
		cerr << "Line(" << __LINE__ << ") -> function(" << __FUNCTION__                \
		     << ") -> CHK FAILED: (" << #__VA_ARGS__ << ")" << "\n",                   \
		    exit(0);
#else
#define dbg(...) 0
#define chk(...) 0
#endif
 
void setPrec() { cout << fixed << setprecision(15); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
// FILE I/O
void setIn(str s) { freopen(s.c_str(), "r", stdin); }
void setOut(str s) { freopen(s.c_str(), "w", stdout); }
void setIO(str s = "") {
	unsyncIO();
	setPrec();
	// cin.exceptions(cin.failbit);
	// throws exception when do smth illegal
	// ex. try to read letter into int
	if (sz(s)) setIn(s + ".in"), setOut(s + ".out");  // for USACO
}
 
void ad(vi &a, int b) {
	ckmin(b, sz(a) - 1);
	if (b < 0) return;
	a[b]++;
}
int get(vi &a, int b) {
	assert(b >= 0 && b < sz(a));
	return a[b];
}
void prop(vi &a) { R0F(i, sz(a) - 1) a[i] += a[i + 1]; }
 
vi adj[MX];
 
template <int SZ> struct Centroid {
	int N;
	bool done[SZ];                          // processed as centroid yet
	int sub[SZ], cen[SZ], lev[SZ], mn[SZ];  // subtree size
	vi stor[SZ], STOR[SZ];                  // STOR removes overcount
	void dfs(int x, int p) {
		sub[x] = 1;
		trav(y, adj[x]) if (!done[y] && y != p) {
			dfs(y, x);
			sub[x] += sub[y];
		}
	}
	int centroid(int x) {
		dfs(x, -1);
		for (int sz = sub[x];;) {
			pi mx = {0, 0};
			trav(y, adj[x]) if (!done[y] && sub[y] < sub[x]) ckmax(mx, {sub[y], y});
			if (mx.f * 2 <= sz) return x;
			x = mx.s;
		}
	}
	vector<vi> dist;  // dists to all centroid ancs
	void genDist(int x, int p, int lev) {
		dist[lev][x] = dist[lev][p] + 1;
		trav(y, adj[x]) if (!done[y] && y != p) genDist(y, x, lev);
	}  // CEN = {centroid above x, label of centroid subtree}
	void gen(int CEN, int _x) {
		int x = centroid(_x);
		done[x] = 1;
		cen[x] = CEN;
		sub[x] = sub[_x];
		lev[x] = (CEN == -1 ? 0 : lev[CEN] + 1);
		stor[x].rsz(sub[x]), STOR[x].rsz(sub[x] + 1);
		dbg("HA", x, sub[x]);
		if (lev[x] >= sz(dist)) dist.eb(N + 1, -1);
		dist[lev[x]][x] = 0;
		mn[x] = MOD;
		trav(y, adj[x]) if (!done[y]) genDist(y, x, lev[x]);
		trav(y, adj[x]) if (!done[y]) gen(x, y);
	}
	void init(int _N) {
		N = _N;
		gen(-1, 1);
	}  // start with vertex 1
	void upd(int x, int y) {
		int cur = x, pre = -1;
		R0F(i, lev[x] + 1) {
			ad(stor[cur], y - dist[i][x]);
			if (pre != -1) ad(STOR[pre], y - dist[i][x]);
			if (i > 0) pre = cur, cur = cen[cur];
		}
	}
	void propAll() { FOR(i, 1, N + 1) prop(stor[i]), prop(STOR[i]); }
	int query(int x) {  // query value at vertex
		int cur = x, pre = -1, ans = 0;
		R0F(i, lev[x] + 1) {
			ans += get(stor[cur], dist[i][x]);
			if (pre != -1) ans -= get(STOR[pre], dist[i][x]);
			if (i > 0) pre = cur, cur = cen[cur];
		}
		return ans;
	}
};
 
/**
 * Description: Calculates least common ancestor in tree
 * with root $R$ using binary jumping.
 * Time: O(N\log N) build, O(\log N) query
 * Source: USACO Camp
 * Verification: Debug the Bugs
 */
 
template <int SZ> struct LCA {
	static const int BITS = 32 - __builtin_clz(SZ);
	int N, R = 1, par[BITS][SZ], depth[SZ];  // vi adj[SZ];
	/// INITIALIZE
	void ae(int u, int v) { adj[u].pb(v), adj[v].pb(u); }
	void dfs(int u, int prv) {
		depth[u] = depth[par[0][u] = prv] + 1;
		trav(v, adj[u]) if (v != prv) dfs(v, u);
	}
	void init(int _N) {
		N = _N;
		dfs(R, 0);
		FOR(k, 1, BITS) FOR(i, 1, N + 1) par[k][i] = par[k - 1][par[k - 1][i]];
	}
	/// QUERY
	int getPar(int a, int b) {
		R0F(k, BITS) if (b & (1 << k)) a = par[k][a];
		return a;
	}
	int lca(int u, int v) {
		if (depth[u] < depth[v]) swap(u, v);
		u = getPar(u, depth[u] - depth[v]);
		R0F(k, BITS) if (par[k][u] != par[k][v]) u = par[k][u], v = par[k][v];
		return u == v ? u : par[0][u];
	}
	int dist(int u, int v) {  // # edges on path
		return depth[u] + depth[v] - 2 * depth[lca(u, v)];
	}
};
 
LCA<MX> L;
Centroid<MX> C;
int close[MX];
int N, K;
 
void dfs1(int x, int p = 0) {
	trav(t, adj[x]) if (t != p) {
		dfs1(t, x);
		ckmin(close[x], close[t] + 1);
	}
}
 
void dfs2(int x, int p = 0) {
	trav(t, adj[x]) if (t != p) {
		ckmin(close[t], close[x] + 1);
		dfs2(t, x);
	}
}
 
void init() {
	setIO();
	re(N, K);
	F0R(i, N - 1) {
		int x, y;
		re(x, y);
		adj[x].pb(y), adj[y].pb(x);
	}
	L.init(N);
	C.init(N);
	FOR(i, 1, N + 1) close[i] = MOD;
	vi a(K);
	re(a);
	trav(t, a) close[t] = 0;
	dfs1(1);
	dfs2(1);
}
 
int main() {
	init();
	FOR(i, 1, N + 1) {
		int f, p;
		re(f, p);
		int d = L.dist(i, f);
		if (d <= close[i] + p) {
			C.upd(i, d - p - 1);
		} else {
			C.upd(i, close[i]);
		}
	}
	C.propAll();
	FOR(i, 1, N + 1) {
		int t = C.query(i);
		pr(t, ' ');
	}
	ps();
}