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
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
#include "bits/stdc++.h" // Tomasz Nowak
using namespace std;     // University of Warsaw
using LL = long long;
#define FOR(i, l, r) for(int i = (l); i <= (r); ++i)
#define REP(i, n) FOR(i, 0, (n) - 1)
#define ssize(x) int(x.size())
template<class A, class B> auto& operator<<(ostream &o, pair<A, B> p) {
	return o << '(' << p.first << ", " << p.second << ')';
}
template<class T> auto operator<<(ostream &o, T x) -> decltype(x.end(), o) {
	o << '{'; int i = 0; for(auto e : x) o << (", ")+2*!i++ << e; return o << '}';
}
#ifdef DEBUG
#define debug(x...) cerr << "[" #x "]: ", [](auto... $) {((cerr << $ << "; "), ...); }(x), cerr << '\n'
#else
#define debug(...) {}
#endif

vector<int> global_deg;
vector<vector<int>> global_graph;
vector<bool> global_vis;
vector<int> global_ans;

void backtrack(
		int remaining_k, 
		vector<bool> &deleted_v, 
		const vector<pair<int, int>> &edges) {
	int n = ssize(deleted_v);
	if(remaining_k < 0)
		return;
	debug(remaining_k, deleted_v, edges);

	fill(global_deg.begin(), global_deg.end(), 0);
	for(auto [v0, v1] : edges)
		if(not deleted_v[v0] and not deleted_v[v1])
			for(int v : {v0, v1})
				++global_deg[v];

	int max_deg_v = int(max_element(global_deg.begin(), global_deg.end()) - global_deg.begin());
	int deg1_v = -1;
	REP(v, n)
		if(global_deg[v] == 1)
			deg1_v = v;
	debug(global_deg[max_deg_v], deg1_v);

	auto save_current_state = [&] {
		int in_ans = accumulate(deleted_v.begin(), deleted_v.end(), 0);
		if(in_ans < ssize(global_ans)) {
			global_ans.clear();
			REP(v, n)
				if(deleted_v[v])
					global_ans.emplace_back(v);
		}
	};

	if(global_deg[max_deg_v] == 0) {
		save_current_state();
		return;
	}
	if(remaining_k == 0)
		return;
	REP(v, n)
		global_graph[v].clear();
	for(auto [v, u] : edges)
		if(not deleted_v[v] and not deleted_v[u]) {
			global_graph[v].emplace_back(u);
			global_graph[u].emplace_back(v);
		}
	if(deg1_v != -1) {
		int u = global_graph[deg1_v][0];
		deleted_v[u] = true;
		backtrack(remaining_k - 1, deleted_v, edges);
		deleted_v[u] = false;
		return;
	}
	if(global_deg[max_deg_v] <= 2) {
		fill(global_vis.begin(), global_vis.end(), false);
		static vector<vector<int>> paths_or_cycles;
		paths_or_cycles.clear();
		function<void (int)> dfs = [&](int s) {
			paths_or_cycles.back().emplace_back(s);
			global_vis[s] = true;
			for(int u : global_graph[s])
				if(not global_vis[u])
					dfs(u);
		};
		REP(v, n)
			if(not global_vis[v] and global_deg[v] == 1) {
				paths_or_cycles.emplace_back();
				dfs(v);
			}
		REP(v, n)
			if(not global_vis[v] and global_deg[v] == 2) {
				paths_or_cycles.emplace_back();
				dfs(v);
			}
		static vector<int> to_del;
		to_del.clear();
		for(auto &path_or_cycle : paths_or_cycles)
			for(int i = bool(global_deg[path_or_cycle[0]] == 1); i < ssize(path_or_cycle); i += 2)
				to_del.emplace_back(path_or_cycle[i]);
		if(ssize(to_del) <= remaining_k) {
			for(int v : to_del)
				deleted_v[v] = true;
			save_current_state();
			for(int v : to_del)
				deleted_v[v] = false;
		}
		return;
	}

	vector<int> neighbors = global_graph[max_deg_v];
	deleted_v[max_deg_v] = true;
	backtrack(remaining_k - 1, deleted_v, edges);
	deleted_v[max_deg_v] = false;
	for(int u : neighbors)
		deleted_v[u] = true;
	backtrack(remaining_k - ssize(neighbors), deleted_v, edges);
	for(int u : neighbors)
		deleted_v[u] = false;
}

int main() {
	cin.tie(0)->sync_with_stdio(0);

	int t;
	cin >> t;
	while(t --> 0) {
		int n, m, k;
		cin >> n >> m >> k;
		vector<pair<int, int>> edges(m);
		for(auto &[v, u] : edges) {
			cin >> v >> u;
			--v, --u;
			if(v > u)
				swap(v, u);
		}
		sort(edges.begin(), edges.end());
		edges.erase(unique(edges.begin(), edges.end()), edges.end());

		vector<int> deg(n);
		for(auto [v, u] : edges) {
			++deg[v];
			++deg[u];
		}
		debug(deg);
		vector<int> output_must_take;
		vector<int> new_id(n, -1);
		int smaller_n = 0;
		int smaller_k = k;
		REP(v, n)
			if(deg[v] > k) {
				output_must_take.emplace_back(v);
				--smaller_k;
			}
			else if(deg[v] > 0)
				new_id[v] = smaller_n++;
		debug(k, output_must_take);
		if(ssize(output_must_take) > k) {
			cout << "-1\n";
			continue;
		}

		vector<pair<int, int>> smaller_edges;
		for(auto [v, u] : edges) {
			v = new_id[v];
			u = new_id[u];
			if(v != -1 and u != -1)
				smaller_edges.emplace_back(v, u);
		}
		debug(smaller_n, smaller_k, smaller_edges);

		global_deg.assign(smaller_n, 0);
		global_graph.assign(smaller_n, vector<int>(smaller_n));
		global_vis.assign(smaller_n, false);

		int best_smaller_size = smaller_n + 1;
		vector<bool> in_some_best(smaller_n);

		if(smaller_edges.empty())
			best_smaller_size = 0;
		else if(smaller_k > 0) {
			vector<bool> deleted_v(smaller_n);
			global_ans.assign(smaller_n + 1, -1);
			backtrack(smaller_k, deleted_v, smaller_edges);
			debug("root", global_ans, deleted_v);
			best_smaller_size = ssize(global_ans);

			if(best_smaller_size < smaller_n + 1) {
				for(int v : global_ans)
					in_some_best[v] = true;
				REP(which_taking_v, smaller_n)
					if(not in_some_best[which_taking_v]) {
						deleted_v[which_taking_v] = true;

						global_ans.assign(smaller_n + 1, -1);
						backtrack(best_smaller_size - 1, deleted_v, smaller_edges);
						int sz = ssize(global_ans);

						deleted_v[which_taking_v] = false;
						debug(which_taking_v, sz);
						if(sz == best_smaller_size) {
							in_some_best[which_taking_v] = true;
							for(int u : global_ans)
								in_some_best[u] = true;
						}
					}
			}
		}
		if(best_smaller_size >= smaller_n + 1) {
			cout << "-1\n";
			continue;
		}

		vector<int> old_id(smaller_n, -1);
		REP(v, n)
			if(new_id[v] != -1)
				old_id[new_id[v]] = v;
		vector<int> output = output_must_take;
		REP(v, smaller_n)
			if(in_some_best[v])
				output.emplace_back(old_id[v]);

		sort(output.begin(), output.end());
		cout << best_smaller_size + ssize(output_must_take) << ' ' << ssize(output) << '\n';
		for(int v : output)
			cout << v + 1 << ' ';
		cout << '\n';
	}
}