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
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
#include <bits/stdc++.h>

#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size())

using namespace std;

#ifdef LOCAL
template<typename A, typename B>
auto&operator<<(auto&o,pair<A, B>p){return o<<"("<<p.first<<", "<<p.second<<")";}
auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<&","[!i++]<<e;return o<<"}";}
#define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X)
#else
#define debug(...){}
#endif

using i64 = long long;
using ll = long long;
#define int i64
using pii = pair<int, int>;
using pll = pair<i64, i64>;
using vi = vector<int>;
using vll = vector<i64>;

const i64 INF = 2e18;

template <typename Tp>
void maxi(Tp &a, Tp b) { a = max(a, b); }

int T = 1;

struct MajorizationContainer {
	MajorizationContainer() {}

	vector<pll> items;

	void AddPair(i64 a, i64 b) {
		items.emplace_back(a, b);
	}

	void Process() {
		sort(ALL(items));
		vector<pll> res;
		for (const auto [a, b] : items) {
			while (!res.empty() && res.back().first <= a && res.back().second <= b) {
				res.pop_back();
			}
			res.emplace_back(a, b);
		}
		swap(items, res);
	}

	bool IsMajorized(i64 a, i64 b) const {
		pll cand{a, b};
		const auto iter = lower_bound(ALL(items), cand);
		if (iter == items.end()) {
			return false;
		}
		return (iter->first >= a && iter->second >= b);
	}
};

struct UnsortedLBSearcher {
	int base;
	vll data;

	UnsortedLBSearcher() {}

	UnsortedLBSearcher(const vll &items) {
		const int n = SZ(items);
		base = 1;
		while (base < n + 5) { base *= 2; }
		data.resize(base * 2, -INF);

		for (int i = 0; i < n; ++i) {
			data[i + base] = items[i];
		}
		data[n + base] = INF;
		for (int i = base - 1; i > 0; --i) {
			data[i] = max(data[i * 2], data[i * 2 + 1]);
		}
	}

	int FirstGeqOnSuffix(int start, i64 x) const {
		int v = start + base;
		while (data[v] < x) {
			if (v % 2 == 1) { ++v; }
			v /= 2;
			assert(v);
		}
		while (v < base) {
			if (data[v * 2] >= x) {
				v *= 2;
			} else {
				v = v * 2 + 1;
			}
			assert(data[v] >= x);
		}
		return v - base;
	}
};

struct APlusBSearcher {
	int base;
	struct Node {
		i64 max_a = -INF, max_b = -INF, max_aplusb = -INF;
		const Node Merge(const Node &rhs) const {
			Node ans;
			ans.max_a = max(max_a, rhs.max_a);
			ans.max_b = max(max_b, rhs.max_b);
			ans.max_aplusb = max({max_aplusb, rhs.max_aplusb, max_a + rhs.max_b});
			return ans;
		}
	};

	vector<Node> data;

	APlusBSearcher() {}
	APlusBSearcher(const vll &A, const vll &B) {
		debug("APlusBSearcher", A, B);
		const int n = SZ(A);
		base = 1;
		while (base < n + 5) { base *= 2; }
		data.resize(base * 2);

		for (int i = 0; i < n; ++i) {
			data[i + base].max_a = A[i];
			data[i + base].max_b = B[i];
		}
		data[n + base].max_aplusb = INF;
		for (int i = base - 1; i > 0; --i) {
			data[i] = data[i * 2].Merge(data[i * 2 + 1]);
		}
	}

	int FirstStopWithAPlusBGeqX(int start, i64 x) const {
		debug("APlusBSearch-Query", start, x);
		Node cur_pref;
		int v = start + base;
		while (cur_pref.Merge(data[v]).max_aplusb < x) {
			if (v % 2 == 1) {
				cur_pref = cur_pref.Merge(data[v]);
				++v;
			}
			v /= 2;
			assert(v);
		}
		debug(base, v);
		while (v < base) {
			const Node &cand_pref = cur_pref.Merge(data[v * 2]);
			if (cand_pref.max_aplusb >= x) {
				v *= 2;
			} else {
				cur_pref = cand_pref;
				v = v * 2 + 1;
			}
			assert(cur_pref.Merge(data[v]).max_aplusb >= x);
		}
		const int ans = v - base;
		debug(ans);
		return v - base;
	}
};

struct Testcase {
	int n, q, sz;
	struct Edge {
		int to;
		i64 cost;
	};
	vector<vector<Edge>> graph;
	vll parent;
	vll diameter;
	vll diameter_pos;
	vll dist_to_diameter;
	vll diameter_repr;
	vll depth;

	vll longest_rooted_path_dn;
	vll longest_inside_path_dn;
	vll longest_outside_path_dn;
	vll longest_rooted_path_up;

	MajorizationContainer path_pairs_all, path_pairs_nodiag;
	vector<MajorizationContainer> cloned_subtree_pairs;
	ll best_nodiag;

	void AddEdge(int u, int v, i64 c) {
		// debug(u, v, c);
		graph[u].push_back({.to = v, .cost = c});
		graph[v].push_back({.to = u, .cost = c});
	}

	void Input() {
		cin >> n;
		if (n < 0) { // FUNNY HACK
			assert(T == 1);
			T = -n;
			cin >> n;
		}
		cin >> q;

		graph.resize(n + 1);
		for (int i = 0; i < n - 1; ++i) {
			int u, v;
			i64 c;
			cin >> u >> v >> c;
			AddEdge(u, v, c);
		}
	}

	int FindFarthest(int v) {
		function<pair<int, i64>(int, int)> Dfs = [&](int v, int p) {
			pair<int, i64> ans{v, 0};
			for (const auto &edge : graph[v]) {
				if (edge.to == p) { continue; }
				auto [s, d] = Dfs(edge.to, v);
				d += edge.cost;
				if (d > ans.second) {
					ans = {s, d};
				}
			}
			return ans;
		};

		return Dfs(v, -1).first;
	}

	vll FindPath(int a, int b) {
		vll ans;
		function<bool(int, int)> Dfs = [&](int v, int p) {
			if (v == a) {
				ans.push_back(a);
				return true;
			}
			for (const auto &edge : graph[v]) {
				if (edge.to == p) { continue; }
				if (Dfs(edge.to, v)) {
					ans.push_back(v);
					return true;
				}
			}
			return false;
		};
		const bool ret = Dfs(b, -1);
		assert(ret);
		return ans;
	}

	void DfsBasicDiameterDepth(int v, int p) {
		for (const auto &edge : graph[v]) {
			if (edge.to == p) { continue; }
			depth[edge.to] = depth[v] + edge.cost;
			if (diameter_pos[edge.to] == -1) {
				diameter_repr[edge.to] = diameter_repr[v];
				dist_to_diameter[edge.to] = dist_to_diameter[v] + edge.cost;
			}
			DfsBasicDiameterDepth(edge.to, v);
		}
	}

	void CloneSubtree(int diameter_vtx, int branch, i64 first_cost) {
		function<void(int, int)> Dfs = [&](int v, int p) {
			for (const auto &edge : graph[v]) {
				const int s = edge.to;
				if (s == p) { continue; }

				const int nv = v + n;
				const int ns = s + n;
				AddEdge(nv, ns, edge.cost);
				depth[ns] = depth[nv] + edge.cost;
				Dfs(s, v);
			}
		};

		const int nr = branch + n;
		const int nd = nr + n;
		debug("Clone", nd, nr, first_cost);
		AddEdge(nd, nr, first_cost);
		depth[nd] = 0;
		depth[nr] = first_cost;
		Dfs(branch, diameter_vtx);
	}

	void FindAndProcessDiameter() {
		const int diam_end1 = FindFarthest(1);
		const int diam_end2 = FindFarthest(diam_end1);
		diameter = FindPath(diam_end1, diam_end2);
		debug(diameter);

		diameter_pos.resize(n + 1, -1);
		diameter_repr.resize(n + 1, -1);
		for (int i = 0; i < SZ(diameter); ++i) {
			diameter_pos[diameter[i]] = i;
			diameter_repr[diameter[i]] = diameter[i];
		}
		dist_to_diameter.resize(n + 1);
		depth.resize(n + 1);
		DfsBasicDiameterDepth(diam_end1, -1);

		debug(diameter_pos);
		debug(diameter_repr);
		debug(dist_to_diameter);
		debug(depth);

		graph.resize(3 * n + 1);
		parent.resize(3 * n + 1);
		depth.resize(3 * n + 1);
		sz = 3 * n;

		for (int v : diameter) {
			for (const auto &edge : graph[v]) {
				const int s = edge.to;
				if (diameter_pos[s] != -1) { continue; }
				CloneSubtree(v, s, edge.cost);
			}
		}
	}

	void FindLongSubtreePaths() {
		longest_inside_path_dn.resize(sz + 1, -1);
		longest_outside_path_dn.resize(sz + 1, -1);
		longest_rooted_path_dn.resize(sz + 1, -1);
		longest_rooted_path_up.resize(sz + 1, -1);
		vector<vll> rooted_cand_lists(sz + 1);
		vector<vll> inside_cand_lists(sz + 1);

		function<void(int, int)> DfsDn = [&](int v, int p) {
			parent[v] = p;
			longest_rooted_path_dn[v] = longest_inside_path_dn[v] = 0;

			for (const auto &edge : graph[v]) {
				if (edge.to == p) { continue; }
				const int s = edge.to;
				DfsDn(s, v);
				const i64 cand = longest_rooted_path_dn[s] + edge.cost;
				maxi(longest_rooted_path_dn[v], cand);
				maxi(longest_inside_path_dn[v], longest_inside_path_dn[s]);
				rooted_cand_lists[v].push_back(cand);
				inside_cand_lists[v].push_back(longest_inside_path_dn[s]);
			}

			sort(ALL(rooted_cand_lists[v]), greater<i64>());
			sort(ALL(inside_cand_lists[v]), greater<i64>());
			if (!rooted_cand_lists[v].empty()) {
				maxi(longest_inside_path_dn[v], rooted_cand_lists[v][0]);
			}
			if (SZ(rooted_cand_lists[v]) >= 2) {
				maxi(longest_inside_path_dn[v], rooted_cand_lists[v][0] + rooted_cand_lists[v][1]);
			}
			debug(v, longest_rooted_path_dn[v], rooted_cand_lists[v], longest_inside_path_dn[v]);
		};

		function<void(int, int, i64)> DfsUp = [&](int v, int p, i64 cur_up_rooted) {
			debug(v, p, cur_up_rooted, longest_outside_path_dn[v]);
			longest_rooted_path_up[v] = cur_up_rooted;
			if (p != -1) {
				rooted_cand_lists[v].push_back(cur_up_rooted);
				sort(ALL(rooted_cand_lists[v]), greater<i64>());
			}
			debug(inside_cand_lists[v]);

			for (const auto &edge : graph[v]) {
				if (edge.to == p) { continue; }
				const int s = edge.to;

				maxi(longest_outside_path_dn[s], longest_outside_path_dn[v]);
				if (inside_cand_lists[v][0] != longest_inside_path_dn[s]) {
					maxi(longest_outside_path_dn[s], inside_cand_lists[v][0]);
				} else if (SZ(inside_cand_lists[v]) >= 2) {
					maxi(longest_outside_path_dn[s], inside_cand_lists[v][1]);
				}

				i64 next_up_rooted = 0;
				i64 outside_cand = 0;
				int num_used = 0;
				bool is_skipped = false;
				const i64 skip_cand = longest_rooted_path_dn[s] + edge.cost;
				for (i64 cand : rooted_cand_lists[v]) {
					if (cand == skip_cand && !is_skipped) {
						is_skipped = true;
					} else {
						if (num_used == 0) { next_up_rooted = cand; }
						outside_cand += cand;
						++num_used;
						if (num_used == 2) { break; }
					}
				}
				maxi(longest_outside_path_dn[s], outside_cand);

				DfsUp(s, v, next_up_rooted + edge.cost);
			}
		};

		DfsDn(diameter[0], -1);
		DfsUp(diameter[0], -1, 0);
		for (int i = 2 * n + 1; i <= 3 * n; ++i) {
			DfsDn(i, -1);
			DfsUp(i, -1, 0);
		}
	}

	void PreprocOneAndTwoPathCases() {
		auto AddCand = [&](MajorizationContainer &dest, i64 a, i64 b) {
			if (a < b) { swap(a, b); }
			dest.AddPair(a, b);
		};

		auto AddCandForEdge = [&](MajorizationContainer &dest, int v) {
			const int pnt = parent[v];
			const i64 edge_len = depth[v] - depth[pnt];
			AddCand(dest, longest_inside_path_dn[v], longest_outside_path_dn[v]);
			AddCand(dest, longest_rooted_path_dn[v] + edge_len, longest_outside_path_dn[v]);
			AddCand(dest, longest_inside_path_dn[v], longest_rooted_path_up[v]);
		};

		for (int v = 1; v <= n; ++v) {
			if (v != diameter[0]) {
				AddCandForEdge(path_pairs_all, v);
			}
		}
		path_pairs_all.Process();
		debug(path_pairs_all.items);

		best_nodiag = 0;

		vll single_paths(2);
		for (int v = 2 * n + 1; v <= 3 * n; ++v) {
			single_paths.push_back(longest_inside_path_dn[v]);
		}
		for (int v = 1; v <= n; ++v) {
			if (diameter_pos[v] == -1) {
				AddCandForEdge(path_pairs_nodiag, v + n);
			}
		}
		sort(ALL(single_paths), greater<i64>());
		best_nodiag = single_paths[0];
		path_pairs_nodiag.AddPair(single_paths[0], single_paths[1]);
		path_pairs_nodiag.Process();
		debug(path_pairs_nodiag.items);
		debug(best_nodiag);
	}

	bool ContainsPathPair(i64 L1, i64 L2, MajorizationContainer &search_target) {
		if (L1 < L2) { swap(L1, L2); }
		return search_target.IsMajorized(L1, L2);
	}

	vll search_vertex_start;
	vll search_vertex_end;
	vll search_ends;
	vll search_depth;
	vll search_addlen;
	vll search_vtx;

	struct SearchInsidePaths {
		int idx;
		int vtx_i;
		i64 fit_size;
		bool operator<(const SearchInsidePaths &other) const {
			return fit_size < other.fit_size;
		}
		bool operator>(const SearchInsidePaths &other) const {
			return fit_size > other.fit_size;
		}
	};
	vector<SearchInsidePaths> search_inside_paths;
	UnsortedLBSearcher search_prefix_inside_lb;
	UnsortedLBSearcher search_suffix_inside_lb;
	APlusBSearcher search_aplusb;

	void PreprocDiameterForSearches() {
		search_vertex_start.resize(n + 1, -1);
		search_vertex_end.resize(n + 1, -1);

		auto InjectInfo = [&](i64 diam_repr, i64 v, i64 rooted_len) {
			const i64 idx = SZ(search_vtx);
			search_vtx.push_back(v);
			search_depth.push_back(depth[diam_repr]);
			search_addlen.push_back(rooted_len);
			return idx;
		};

		for (int v : diameter) {
			search_vertex_start[v] = InjectInfo(v, v, 0);
			search_ends.push_back(search_vertex_start[v]);

			for (const auto &edge : graph[v]) {
				const int s = edge.to;
				if (diameter_pos[edge.to] != -1) { continue; }
				InjectInfo(v, s, longest_rooted_path_dn[s + 2 * n]);
			}

			search_vertex_end[v] = InjectInfo(v, v, 0);
			search_ends.push_back(search_vertex_end[v]);
		}

		for (int i = 0; i < SZ(search_vtx); ++i) {
			debug(i, search_vtx[i], search_depth[i], search_addlen[i]);
		}

		cloned_subtree_pairs.resize(3 * n + 1);
		int cur_cloned_root = -1;
		function<void(int, i64)> DfsRootedAndOther = [&](int v, i64 best_other) {
			cloned_subtree_pairs[cur_cloned_root].AddPair(
				depth[v], max(best_other, longest_inside_path_dn[v]));

			vll cands_inside{0};
			vll cands_rooted{0};
			for (const auto &edge : graph[v]) {
				if (edge.to == parent[v]) { continue; }
				cands_inside.push_back(longest_inside_path_dn[edge.to]);
				cands_rooted.push_back(longest_rooted_path_dn[edge.to] + edge.cost);
			}
			sort(ALL(cands_inside), greater<i64>());
			sort(ALL(cands_rooted), greater<i64>());

			for (const auto &edge : graph[v]) {
				if (edge.to == parent[v]) { continue; }

				i64 inside_cand = cands_inside[0];
				if (inside_cand == longest_inside_path_dn[edge.to]) {
					inside_cand = cands_inside[1];
				}
				i64 rooted_cand = cands_rooted[0];
				const i64 rooted_chk = longest_rooted_path_dn[edge.to] + edge.cost;
				if (rooted_cand == rooted_chk) {
					rooted_cand = cands_rooted[1];
				}
				const i64 next_other = max({best_other, inside_cand, rooted_cand});
				DfsRootedAndOther(edge.to, next_other);
			}
		};

		for (int v = 2 * n + 1; v <= 3 * n; ++v) {
			cur_cloned_root = v;
			DfsRootedAndOther(v, 0);
			cloned_subtree_pairs[v].Process();
			debug(v, cloned_subtree_pairs[v].items);
		}

		for (int i = 0; i < SZ(search_vtx); ++i) {
			const int vtx_i = search_vtx[i];
			const int repr_i = diameter_repr[vtx_i];
			if (vtx_i == repr_i) { continue; }
			const i64 fit_size = longest_inside_path_dn[vtx_i + 2 * n];
			search_inside_paths.push_back({.idx = i, .vtx_i = vtx_i, .fit_size = fit_size});
		}
		sort(ALL(search_inside_paths), greater<SearchInsidePaths>());
		if (SZ(search_inside_paths) > 3) {
			search_inside_paths.resize(3);
		}

		vll data_prefix_inside, data_suffix_inside;
		for (int i = 0; i < SZ(search_vtx); ++i) {
			data_prefix_inside.push_back(search_depth[i] + search_addlen[i]);
		}
		for (int i = SZ(search_vtx) - 1; i >= 0; --i) {
			data_suffix_inside.push_back((search_depth.back() - search_depth[i]) + search_addlen[i]);
		}
		search_prefix_inside_lb = UnsortedLBSearcher{data_prefix_inside};
		search_suffix_inside_lb = UnsortedLBSearcher{data_suffix_inside};

		vll aplusb_data_A, aplusb_data_B;
		for (int i = 0; i < SZ(search_vtx); ++i) {
			aplusb_data_A.push_back(search_addlen[i] - search_depth[i]);
			aplusb_data_B.push_back(search_depth[i] + search_addlen[i]);
		}
		search_aplusb = APlusBSearcher(aplusb_data_A, aplusb_data_B);
	}

	i64 SearchRoundToEnd(i64 R) {
		if (R >= SZ(search_vtx)) {
			return SZ(search_vtx);
		}
		R = *lower_bound(ALL(search_ends), R);
		return R;
	}

	int FindFirstOnDiameterOfLength(int start, i64 len) {
		const int ans_fast = search_aplusb.FirstStopWithAPlusBGeqX(start, len);
		// const int ans_slow = FindFirstOnDiameterOfLengthSlow(start, len);
		// debug(ans_fast, ans_slow);
		// assert(ans_fast == ans_slow);
		return ans_fast;
	}

	bool FitsRootedPathAndOtherPath(int root, i64 len_rooted, i64 len_other) {
		return cloned_subtree_pairs[root].IsMajorized(len_rooted, len_other);
	}

	bool SolveQuery(vll lengths) {
		sort(ALL(lengths), greater<i64>());

		// Yes-Case 1: all inside the diameter
		const i64 diam_length = depth[diameter.back()];
		if (lengths[0] + lengths[1] + lengths[2] <= diam_length) {
			debug("Yes-Case 1");
			return true;
		}

		// No-Case 1: lengths[0] doesn't fit the diameter
		if (lengths[0] > diam_length) {
			debug("No-Case 1");
			return false;
		}

		// Yes-Case 2: longest inside the diameter, two other outside the diameter
		if (ContainsPathPair(lengths[1], lengths[2], path_pairs_nodiag)) {
			debug("Yes-Case 2");
			return true;
		}

		// Yes-Case 3: There is some path coupling that works
		for (int outsider : {0, 1, 2}) {
			const i64 path_a = lengths[0] + lengths[1] + lengths[2] - lengths[outsider];
			const i64 path_b = lengths[outsider];
			if (ContainsPathPair(path_a, path_b, path_pairs_all)) {
				debug("Yes-Case 3", outsider, path_a, path_b);
				return true;
			}
		}

		// Yes-Case 4: All three paths intersect the diameter non-trivially
		//   (i.e., containing internally some point of the diameter)
		{
			vll intersect_order = lengths;
			sort(ALL(intersect_order));
			do {
				i64 loc = 0;
				for (i64 len : intersect_order) {
					loc = SearchRoundToEnd(loc);
					loc = FindFirstOnDiameterOfLength(loc, len);
					// debug(intersect_order, len, loc);
				}
				if (loc < SZ(search_vtx)) {
					debug("Yes-Case 4", intersect_order);
					return true;
				}
			} while (next_permutation(ALL(intersect_order)));
		}

		// Yes-Case 5: One path has the start of the diameter, second has the end of the diameter,
		//   the third does not touch the diameter (non-trivially)
		vll path_order = lengths;
		sort(ALL(path_order));
		auto CheckPathOrder = [&]() {
			const i64 len_pref = path_order[0];
			const i64 len_suf = path_order[1];
			const i64 len_inside = path_order[2];

			vector<int> Ls, Rs;
			{
				int cur = 0;
				for (int i = 0; i < 2 && cur < SZ(search_vtx); ++i) {
					const int nxt = search_prefix_inside_lb.FirstGeqOnSuffix(cur, len_pref);
					if (nxt >= SZ(search_vtx)) { break; }
					Ls.push_back(nxt);
					cur = nxt + 1;
				}
			}
			{
				int cur = 0;
				for (int i = 0; i < 2 && cur < SZ(search_vtx); ++i) {
					const int nxt = search_suffix_inside_lb.FirstGeqOnSuffix(cur, len_suf);
					if (nxt >= SZ(search_vtx)) { break; }
					Rs.push_back(SZ(search_vtx) - nxt - 1);
					cur = nxt + 1;
				}
			}
			if (Ls.empty() || Rs.empty()) {
				return false;
			}

			for (int L : Ls) {
				for (int R : Rs) {
					if (L >= R) { continue; }
					const int vtx_L = search_vtx[L];
					const int vtx_R = search_vtx[R];
					const int repr_L = diameter_repr[vtx_L];
					const int repr_R = diameter_repr[vtx_R];
					const bool is_L_down = (repr_L != vtx_L);
					const bool is_R_down = (repr_R != vtx_R);

					if (repr_L == repr_R && is_L_down && is_R_down) {
						continue;
					}

					// debug(path_order, L, R);

					// Yes-Case 5L: the other path sits in a subtree at loc L
					if (is_L_down) {
						const i64 len_rooted = len_pref - search_depth[L];
						if (FitsRootedPathAndOtherPath(vtx_L + 2 * n, len_rooted, len_inside)) {
							debug("Case 5L", vtx_L, repr_L);
							return true;
						}
					}

					// Yes-Case 5R: the other path sits in a subtree at loc R
					if (is_R_down) {
						const i64 len_rooted = len_suf - (search_depth.back() - search_depth[R]);
						if (FitsRootedPathAndOtherPath(vtx_R + 2 * n, len_rooted, len_inside)) {
							debug("Case 5R", vtx_R, repr_R);
							return true;
						}
					}

					// Yes-Case 5X: the other path sits in some different subtree
					for (const auto &sip : search_inside_paths) {
						const int i = sip.idx;
						if (i == L || i == R) { continue; }
						if (sip.fit_size >= len_inside) {
							const int vtx_i = sip.vtx_i;
							debug("Case 5X", vtx_L, vtx_R, vtx_i);
							return true;
						}
					}
				}
			}

			return false;
		};
		do {
			if (CheckPathOrder()) {
				debug("Yes-Case 5", path_order);
				return true;
			}
		} while (next_permutation(ALL(path_order)));

		return false;
	}

	void Run() {
		Input();
		FindAndProcessDiameter();
		FindLongSubtreePaths();
		PreprocOneAndTwoPathCases();
		PreprocDiameterForSearches();

		for (int qid = 0; qid < q; ++qid) {
			i64 L1, L2, L3;
			cin >> L1 >> L2 >> L3;
			cout << (SolveQuery({L1, L2, L3}) ? "TAK\n" : "NIE\n");
		}
	}
};

int32_t main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout << fixed << setprecision(14);
	cerr << fixed << setprecision(6);

	for (int tid = 0; tid < T; ++tid) {
		Testcase{}.Run();
	}
}