#include <bits/stdc++.h>
using namespace std;
using lint = long long;
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
int N, K;
cin >> N >> K;
vector<lint> X(N), Y(N);
for (int i = 0; i < N; i++) {
cin >> X[i] >> Y[i];
}
long long answerScore = 1e18;
vector<array<lint, 4>> answer;
for (int rot = 0; rot < 4; rot++) {
vector<int> sortByX(N);
vector<int> sortByY(N);
iota(begin(sortByX), end(sortByX), 0);
iota(begin(sortByY), end(sortByY), 0);
sort(begin(sortByX), end(sortByX), [&](int i, int j) {
return pair(X[i], Y[i]) < pair(X[j], Y[j]);
});
sort(begin(sortByY), end(sortByY), [&](int i, int j) {
return pair(Y[i], X[i]) < pair(Y[j], X[j]);
});
vector<int> posInSortByX(N);
vector<int> posInSortByY(N);
for (int i = 0; i < N; i++) {
posInSortByX[sortByX[i]] = i;
posInSortByY[sortByY[i]] = i;
}
const auto CountingSort = [&](vector<int> &a, const vector<int> &sorted, const vector<int> &pos) {
static vector<int> res(N);
fill(begin(res), end(res), 0);
for (auto i : a) {
res[pos[i]] = 1;
}
a.clear();
for (int i = 0; i < N; i++) {
if (res[i]) {
a.emplace_back(sorted[i]);
}
}
};
vector<array<lint, 3>> ans;
const auto SolveK1 = [&](vector<int> alive, lint boundLftX, lint boundRgtX, lint boundLftY, lint boundRgtY, int trace) -> lint {
if (alive.empty()) return 0;
lint minX = +2e9;
lint maxX = -2e9;
lint minY = +2e9;
lint maxY = -2e9;
for (auto i : alive) {
minX = min(minX, X[i]);
maxX = max(maxX, X[i]);
minY = min(minY, Y[i]);
maxY = max(maxY, Y[i]);
}
lint len = max({1ll, maxX - minX, maxY - minY});
if (boundRgtX - boundLftX < len) return 1e18;
if (boundRgtY - boundLftY < len) return 1e18;
if (!trace) {
return len;
}
for (auto x : {boundLftX, minX, maxX - len, boundRgtX - len}) if (-3e9 <= x && x <= 3e9) {
if (boundLftX <= x && x + len <= boundRgtX) {
for (auto y : {boundLftY, minY, maxY - len, boundRgtY - len}) if (-3e9 <= y && y <= 3e9) {
if (boundLftY <= y && y + len <= boundRgtY) {
bool bad = false;
for (auto i : alive) {
if (x <= X[i] && X[i] <= x + len && y <= Y[i] && Y[i] <= y + len) {
} else {
bad = true;
break;
}
}
if (!bad) {
ans.push_back({x, y, len});
return len;
}
}
}
}
}
assert(false);
return 1e18;
};
map<tuple<vector<int>, int, lint>, lint> memoK2;
const auto SolveK2 = [&](vector<int> alive, int vert, lint boundLftX, int trace) -> lint {
if (alive.empty()) return 0;
if (auto it = memoK2.find({alive, vert, boundLftX}); trace == 0 && it != end(memoK2)) {
return it->second;
}
lint res = SolveK1(alive, boundLftX, 1e18, -1e18, 1e18, 0);
if (!vert) {
CountingSort(alive, sortByY, posInSortByY);
} else {
CountingSort(alive, sortByX, posInSortByX);
}
static vector<lint> prefMinX(N);
static vector<lint> prefMaxX(N);
static vector<lint> prefMinY(N);
static vector<lint> prefMaxY(N);
static vector<lint> suffMinX(N);
static vector<lint> suffMaxX(N);
static vector<lint> suffMinY(N);
static vector<lint> suffMaxY(N);
for (int i = 0; i < int(alive.size()); i++) {
int id = alive[i];
prefMinX[i] = prefMaxX[i] = X[id];
prefMinY[i] = prefMaxY[i] = Y[id];
suffMinX[i] = suffMaxX[i] = X[id];
suffMinY[i] = suffMaxY[i] = Y[id];
}
for (int i = 1; i < int(alive.size()); i++) {
prefMinX[i] = min(prefMinX[i], prefMinX[i - 1]);
prefMaxX[i] = max(prefMaxX[i], prefMaxX[i - 1]);
prefMinY[i] = min(prefMinY[i], prefMinY[i - 1]);
prefMaxY[i] = max(prefMaxY[i], prefMaxY[i - 1]);
}
for (int i = int(alive.size()) - 2; i >= 0; i--) {
suffMinX[i] = min(suffMinX[i], suffMinX[i + 1]);
suffMaxX[i] = max(suffMaxX[i], suffMaxX[i + 1]);
suffMinY[i] = min(suffMinY[i], suffMinY[i + 1]);
suffMaxY[i] = max(suffMaxY[i], suffMaxY[i + 1]);
}
const auto CalcPref = [&](int i) -> lint {
if (i < 0 || i >= int(alive.size())) return 0;
return max(prefMaxX[i] - prefMinX[i], prefMaxY[i] - prefMinY[i]);
};
const auto CalcSuff = [&](int i) -> lint {
if (i < 0 || i >= int(alive.size())) return 0;
return max(suffMaxX[i] - suffMinX[i], suffMaxY[i] - suffMinY[i]);
};
if (vert == 0) {
for (int i = 0; i < int(alive.size()); i++) {
if (!(i + 1 == int(alive.size()) || Y[alive[i + 1]] != Y[alive[i]])) {
continue;
}
res = min(res, max(CalcPref(i), CalcSuff(i + 1)));
}
if (res == 1e18) {
return memoK2[{alive, vert, boundLftX}] = res;
}
vector<int> pref;
vector<int> suff = alive;
reverse(begin(suff), end(suff));
for (int i = 0; i < int(alive.size()); i++) {
pref.emplace_back(alive[i]);
suff.pop_back();
if (!(i + 1 == int(alive.size()) || Y[alive[i + 1]] != Y[alive[i]])) {
continue;
}
if (res == max(CalcPref(i), CalcSuff(i + 1))) {
SolveK1(pref, boundLftX, 1e18, -1e18, Y[alive[i]], trace);
SolveK1(suff, boundLftX, 1e18, Y[alive[i]] + 1, 1e18, trace);
return memoK2[{alive, vert, boundLftX}] = res;
}
}
} else {
for (int i = 0; i < int(alive.size()); i++) {
if (!(i + 1 == int(alive.size()) || X[alive[i + 1]] != X[alive[i]])) {
continue;
}
lint len = CalcPref(i);
lint upTo = (i + 1 == int(alive.size())) ? 1e18 : (X[alive[i + 1]] - 1);
if (upTo - max(boundLftX, prefMinX[i]) < len) continue;
res = min(res, max(CalcPref(i), CalcSuff(i + 1)));
}
if (res == 1e18) {
return memoK2[{alive, vert, boundLftX}] = res;
}
vector<int> pref;
vector<int> suff = alive;
reverse(begin(suff), end(suff));
for (int i = 0; i < int(alive.size()); i++) {
pref.emplace_back(alive[i]);
suff.pop_back();
if (!(i + 1 == int(alive.size()) || X[alive[i + 1]] != X[alive[i]])) {
continue;
}
lint len = CalcPref(i);
lint upTo = (i + 1 == int(alive.size())) ? 1e18 : (X[alive[i + 1]] - 1);
if (upTo - max(boundLftX, prefMinX[i]) < len) continue;
if (res == max(CalcPref(i), CalcSuff(i + 1))) {
SolveK1(pref, boundLftX, upTo, -1e18, 1e18, trace);
SolveK1(suff, upTo + 1, 1e18, -1e18, 1e18, trace);
return memoK2[{alive, vert, boundLftX}] = res;
}
}
}
if (res == SolveK1(alive, boundLftX, 1e18, -1e18, 1e18, 0)) {
return memoK2[{alive, vert, boundLftX}] = SolveK1(alive, boundLftX, 1e18, -1e18, 1e18, trace);
}
return memoK2[{alive, vert, boundLftX}] = 1e18;
};
const auto SolveK3 = [&](vector<int> alive, int trace) -> lint {
lint res = 1e18;
res = min(res, SolveK2(alive, 0, -1e18, 0));
res = min(res, SolveK2(alive, 1, +1e18, 0));
CountingSort(alive, sortByX, posInSortByX);
static vector<lint> prefMinX(N);
static vector<lint> prefMaxX(N);
static vector<lint> prefMinY(N);
static vector<lint> prefMaxY(N);
for (int i = 0; i < int(alive.size()); i++) {
int id = alive[i];
prefMinX[i] = prefMaxX[i] = X[id];
prefMinY[i] = prefMaxY[i] = Y[id];
}
for (int i = 1; i < int(alive.size()); i++) {
prefMinX[i] = min(prefMinX[i], prefMinX[i - 1]);
prefMaxX[i] = max(prefMaxX[i], prefMaxX[i - 1]);
prefMinY[i] = min(prefMinY[i], prefMinY[i - 1]);
prefMaxY[i] = max(prefMaxY[i], prefMaxY[i - 1]);
}
const auto CalcPref = [&](int i) -> lint {
if (i < 0 || i >= int(alive.size())) return 0;
return max(prefMaxX[i] - prefMinX[i], prefMaxY[i] - prefMinY[i]);
};
vector<lint> coordX = X;
sort(begin(coordX), end(coordX));
coordX.resize(unique(begin(coordX), end(coordX)) - begin(coordX));
const auto Check = [&](lint maxD) -> pair<int, bool> {
int ok = -1;
for (int i = 0; i < int(alive.size()); i++) {
if (!(i + 1 == int(alive.size()) || X[alive[i + 1]] != X[alive[i]])) {
continue;
}
if (CalcPref(i) <= maxD) {
ok = i;
}
}
vector<int> other;
for (int i = ok + 1; i < int(alive.size()); i++) {
other.emplace_back(alive[i]);
}
return {ok, min(SolveK2(other, 0, ok == -1 ? -1e18 : (X[alive[ok]] + 1), 0),
SolveK2(other, 1, ok == -1 ? -1e18 : (X[alive[ok]] + 1), 0)) <= maxD};
};
lint lo = 1, hi = 2e9;
while (lo < hi) {
lint md = (lo + hi) / 2;
if (Check(md).second) {
hi = md;
} else {
lo = md + 1;
}
}
int cand = Check(lo).first;
vector<int> suff = alive;
reverse(begin(suff), end(suff));
for (int i = 0; i < int(alive.size()); i++) {
suff.pop_back();
if (!(i + 1 == int(alive.size()) || X[alive[i + 1]] != X[alive[i]])) {
continue;
}
if (i != cand) continue;
res = min(res, max(CalcPref(i), SolveK2(suff, 0, X[alive[i]] + 1, 0)));
res = min(res, max(CalcPref(i), SolveK2(suff, 1, X[alive[i]] + 1, 0)));
}
if (res == 1e18) {
return res;
}
suff = alive;
vector<int> pref;
reverse(begin(suff), end(suff));
for (int i = 0; i < int(alive.size()); i++) {
pref.emplace_back(alive[i]);
suff.pop_back();
if (!(i + 1 == int(alive.size()) || X[alive[i + 1]] != X[alive[i]])) {
continue;
}
if (i != cand) continue;
if (res == max(CalcPref(i), SolveK2(suff, 0, X[alive[i]] + 1, 0))) {
SolveK1(pref, -1e18, X[alive[i]], -1e18, 1e18, trace);
SolveK2(suff, 0, X[alive[i]] + 1, trace);
return res;
}
if (res == max(CalcPref(i), SolveK2(suff, 1, X[alive[i]] + 1, 0))) {
SolveK1(pref, -1e18, X[alive[i]], -1e18, 1e18, trace);
SolveK2(suff, 1, X[alive[i]] + 1, trace);
return res;
}
}
if (res == SolveK2(alive, 0, -1e18, 0)) {
return SolveK2(alive, 0, -1e18, trace);
}
if (res == SolveK2(alive, 1, -1e18, 0)) {
return SolveK2(alive, 1, -1e18, trace);
}
return 1e18;
};
const auto Solve = [&](int K, int trace) -> lint {
vector<int> alive(N);
iota(begin(alive), end(alive), 0);
if (K == 1) {
ans.clear();
return SolveK1(alive, -1e18, 1e18, -1e18, 1e18, trace);
} else if (K == 2) {
ans.clear();
lint res1 = SolveK2(alive, 0, -1e18, trace);
auto ans1 = ans;
ans.clear();
lint res2 = SolveK2(alive, 1, -1e18, trace);
auto ans2 = ans;
if (res1 < res2) {
ans = ans1;
return res1;
} else {
ans = ans2;
return res2;
}
} else if (K == 3) {
ans.clear();
return SolveK3(alive, trace);
} else {
assert(false);
return -1;
}
};
lint res = Solve(K, 1);
if (res < answerScore) {
answerScore = res;
answer.clear();
for (auto &a : ans) {
answer.push_back({a[0], a[1], a[0] + a[2], a[1] + a[2]});
}
}
for (int i = 0; i < N; i++) {
swap(X[i], Y[i]); Y[i] *= -1;
}
for (int i = 0; i < int(answer.size()); i++) {
swap(answer[i][0], answer[i][1]); answer[i][1] *= -1;
swap(answer[i][2], answer[i][3]); answer[i][3] *= -1;
}
}
vector<array<lint, 3>> ans;
for (auto a : answer) {
if (a[0] > a[2]) swap(a[0], a[2]);
if (a[1] > a[3]) swap(a[1], a[3]);
assert(a[2] - a[0] == a[3] - a[1]);
ans.push_back({a[0], a[1], a[2] - a[0]});
}
int it = 0;
while (int(ans.size()) < K) {
ans.push_back({lint(-3e9 + 2 * it), lint(3e9), 1});
it++;
}
const auto ValidAnswer = [&](vector<array<lint, 3>> sq) {
assert(int(sq.size()) <= K);
for (int i = 0; i < int(sq.size()); i++) {
for (int j = 0; j < int(sq.size()); j++) if (i != j) {
for (auto x : {sq[j][0], sq[j][0] + sq[j][2]}) {
for (auto y : {sq[j][1], sq[j][1] + sq[j][2]}) {
lint minX = sq[i][0];
lint maxX = sq[i][0] + sq[i][2];
lint minY = sq[i][1];
lint maxY = sq[i][1] + sq[i][2];
if (minX <= x && x <= maxX && minY <= y && y <= maxY) {
return false;
}
}
}
}
}
for (int i = 0; i < N; i++) {
bool found = false;
for (auto [x, y, l] : sq) {
if (x <= X[i] && X[i] <= x + l && y <= Y[i] && Y[i] <= y + l) {
found = true;
break;
}
}
if (!found) {
return false;
}
}
return true;
};
assert(ValidAnswer(ans));
for (int i = 0; i < K; i++) {
cout << ans[i][0] << ' ' << ans[i][1] << ' ' << ans[i][2] << '\n';
}
return 0;
}
