1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
#include <bits/stdc++.h>
using namespace std;
#define PII pair<int, int>
#define VI vector<int>
#define VPII vector<PII>
#define LL long long
#define LD long double
#define f first
#define s second
#define MP make_pair
#define PB push_back
#define endl '\n'
#define ALL(c) (c).begin(), (c).end()
#define SIZ(c) (int)(c).size()
#define REP(i, n) for(int i = 0; i < (int)(n); ++i)
#define FOR(i, b, e) for(int i = (b); i <= (int)(e); ++i)
#define FORD(i, b, e) for(int i = (b); i >= (int)(e); --i)
#define ll LL
#define st f
#define nd s
#define pb PB
#define mp MP
#define eb emplace_back
#define siz(c) SIZ(c)
const int inf = 1e9+7;
const ll INF = 1e18L+7;

#define sim template<class n
sim, class s> ostream & operator << (ostream &p, pair<n, s> x)
{return p << "<" << x.f << ", " << x.s << ">";}
sim> auto operator << (ostream &p, n y) ->
typename enable_if<!is_same<n, string>::value, decltype(y.begin(), p)>::type 
{int o = 0; p << "{"; for(auto c: y) {if(o++) p << ", "; p << c;} return p << "}";}
void dor() {cerr << endl;}
sim, class...s> void dor(n p, s...y) {cerr << p << " "; dor(y...);}
sim, class s> void mini(n &p, s y) {if(p>y) p = y;}
sim, class s> void maxi(n &p, s y) {if(p<y) p = y;}
#ifdef DEB
#define debug(...) dor(__FUNCTION__, ":", __LINE__, ": ", __VA_ARGS__)
#else
#define debug(...)
#endif 

#define I(x) #x " =", (x), " "

#ifndef LOCAL
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace __gnu_pbds;

template <typename T>
using ordered_set =
	tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

#else
#include</Users/dawid/algo/mac/ordered_set>
#endif

const int N = 307;

int n;

VI G[N];

ll a[N];

bitset<N> vis;

vector<pair<ll, ll> > dp[2][N][N]; // <score, this component sum>

void clear() {
	vis.reset();

	for (int i = 0; i < N; ++i) {
		G[i].clear();

		for (int j = 0; j < N; ++j) {
			dp[0][i][j].clear();
			dp[1][i][j].clear();
		}
	}
}	

void hull(vector<pair<ll, ll> > &vec) {
	sort(ALL(vec));

	vector<pair<ll, ll > > new_vec;

	for (auto it : vec) {
		if (new_vec.empty()) {
			new_vec.pb(it);
		} else {
			if (it.st == new_vec.back().st)
				mini(new_vec.back().nd, it.nd);
			else if (it.nd < new_vec.back().nd)
				new_vec.pb(it);
		}
	}

	vec = new_vec;
}

void dfs(int v) {
	vis[v] = 1;

	dp[0][v][0] = {{a[v] * a[v], a[v]}};

	for (auto u : G[v]) {
		if (!vis[u]) {
			dfs(u);

			for (int i = 0; i <= n - 1; ++i) {
				for (int j = 0; i + j <= n - 1; ++j) {
					for (auto fv : dp[0][v][i]) {
						for (auto fu : dp[0][u][j]) {
							ll new_score = fv.st + fu.st + 2 * fv.nd * fu.nd;
							ll new_comp = fv.nd + fu.nd;
							dp[1][v][i + j].emplace_back(new_score, new_comp);

							new_score = fv.st + fu.st;
							new_comp = fv.nd;
							dp[1][v][i + j + 1].emplace_back(new_score, new_comp);
						}
					}
				}
			}

			for (int i = 0; i <= n - 1; ++i) {
				hull(dp[1][v][i]);
				dp[0][v][i] = dp[1][v][i];
				dp[1][v][i].clear();
			}
		}
	}
}

void solve() {
	cin >> n;

	for (int i = 1; i <= n; ++i) {
		cin >> a[i];
	}

	for (int i = 1; i < n; ++i) {
		int a, b;
		cin >> a >> b;
		G[a].pb(b);
		G[b].pb(a);
	}

	dfs(1);

	for (int i = 1; i <= n; ++i) {
		cout << dp[0][1][i - 1][0].st << " ";
	}

	cout << endl;

	clear();
}

int32_t main() {
	ios_base::sync_with_stdio(0);
	cin.tie(NULL);

	int t_cases;
	cin >> t_cases;

	while (t_cases--) {
		solve();
	}
}