## Editorial for BARICA

Remember to use this editorial only when stuck, and not to copy-paste code from it. Please be respectful to the problem author and editorialist.
Submitting an official solution before solving the problem yourself is a bannable offence.

Lưu ý: Các code mẫu dưới đây chỉ mang tính tham khảo và có thể không AC được bài tập này

#### Code mẫu của flashmt

const maxn=100010;
var n,k:longint;
x,y,a,d,f:array[1..maxn] of longint;
maxcol:array[0..maxn] of longint;

procedure rf;
var i:longint;
begin
for i:=1 to n do
begin
d[i]:=i;
end;
end;

procedure sort(l,r:longint);
var i,j,t,u,v:longint;
begin
i:=l; j:=r; t:=x[(i+j) shr 1]; v:=y[(i+j) shr 1];
repeat
while (x[i]<t) or ((x[i]=t) and (y[i]<v)) do i:=i+1;
while (x[j]>t) or ((x[j]=t) and (y[j]>v)) do j:=j-1;
if i<=j then
begin
u:=d[i]; d[i]:=d[j]; d[j]:=u;
u:=x[i]; x[i]:=x[j]; x[j]:=u;
u:=y[i]; y[i]:=y[j]; y[j]:=u;
u:=a[i]; a[i]:=a[j]; a[j]:=u;
i:=i+1; j:=j-1;
end;
until i>j;
if i<r then sort(i,r);
if l<j then sort(l,j);
end;

function max(u,v:longint):longint;
begin
if u>v then max:=u else max:=v;
end;

procedure pr;
var i,t,u,maxrow:longint;
begin
sort(1,n);
for i:=1 to n do f[i]:=-1;
for i:=0 to maxn div 3 do maxcol[i]:=-1;
for t:=1 to n do
if d[t]=1 then break;
f[t]:=a[t]; maxcol[y[t]]:=a[t]; maxrow:=a[t]; inc(t);
while true do
begin
if x[t]=x[t-1] then
begin
if maxrow>=k then
f[t]:=max(f[t],maxrow-k+a[t]);
end;
if maxcol[y[t]]>=k then
f[t]:=max(f[t],maxcol[y[t]]-k+a[t]);
if x[t]=x[t-1] then maxrow:=max(maxrow,f[t])
else maxrow:=f[t];
maxcol[y[t]]:=max(maxcol[y[t]],f[t]);
if d[t]=n then break;
t:=t+1;
end;
writeln(f[t]);
end;

begin
rf;
pr;
end.


#### Code mẫu của happyboy99x

#include<cstdio>
#include<algorithm>
using namespace std;

const int N = 300000 + 5, XY = 100000 + 5, INF = 1000000000;
struct plant {
int x, y, f, id;
bool operator < (const plant &o) const {
return x < o.x || x == o.x && y < o.y;
}
} p[N];
int n, k, maxX[XY], maxY[XY], f[N];

void enter() {
scanf("%d%d", &n, &k);
for(int i = 1; i <= n; ++i) {
scanf("%d%d%d", &p[i].x, &p[i].y, &p[i].f);
p[i].id = i;
}
}

void solve() {
sort(p+1, p+n+1); f[0] = -INF;
for(int i = 1; i <= n; ++i) {
int id = p[i].id;
f[id] = -INF; if(id == 1) f[id] = p[i].f;
int xx = maxX[p[i].x], yy = maxY[p[i].y];
if(f[xx] >= k && f[xx] - k + p[i].f > f[id]) f[id] = f[xx] - k + p[i].f;
if(f[yy] >= k && f[yy] - k + p[i].f > f[id]) f[id] = f[yy] - k + p[i].f;
if(f[id] > f[xx]) maxX[p[i].x] = id;
if(f[id] > f[yy]) maxY[p[i].y] = id;
}
printf("%d\n", f[n]);
}

int main() {
enter();
solve();
return 0;
}


#### Code mẫu của ladpro98

program baricavn;//dp
uses    math;
type    e=record
x,y,p,s:longint;
end;
const   maxn=300005;
maxV=100005;
fi='';
var     a:array[1..maxn] of e;
maxCol,maxRow:array[0..maxV] of longint;
n,k:longint;

procedure input;
var     inp:text;
i:longint;
begin
assign(inp,fi);
reset(inp);
for i:=1 to n do
begin
a[i].p:=i;
end;
close(inp);
end;

procedure swap(i,j:longint);
var     t:e;
begin
t:=a[i];
a[i]:=a[j];
a[j]:=t;
end;

procedure sort(l,r:longint);
var     i,j:longint;
p:e;
begin
if l>=r then exit;
i:=l;j:=r;
p:=a[random(r-l+1)+l];
repeat
while (a[i].x<p.x) or ((a[i].x=p.x) and (a[i].y<p.y)) do inc(i);
while (a[j].x>p.x) or ((a[j].x=p.x) and (a[j].y>p.y)) do dec(j);
if i<=j then
begin
if i<j then swap(i,j);
inc(i);
dec(j);
end;
until i>j;
sort(l,j);
sort(i,r);
end;

procedure dp;
var     j,i,t,lx,ly:longint;
begin
for j:=1 to n do
if a[j].p=1 then
begin
maxRow[a[j].x]:=a[j].s;
maxCol[a[j].y]:=a[j].s;
lx:=a[j].x;ly:=a[j].y;
for i:=j+1 to n do
if (a[i].x>=lx) and (a[i].y>=ly) then
if max(maxRow[a[i].x],maxCol[a[i].y])>=k then
begin
t:=max(maxRow[a[i].x],maxCol[a[i].y])-k+a[i].s;
if a[i].p=n then
begin
writeln(t);
exit;
end;
maxRow[a[i].x]:=max(maxRow[a[i].x],t);
maxCol[a[i].y]:=max(maxCol[a[i].y],t);
end;
end;
end;

begin
input;
sort(1,n);
dp;
end.


#### Code mẫu của RR

#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <set>

#define MAXN 300111
#define FOR(i,a,b) for(long i=a; i<=b; i++)
#define S set< pair<long,long> >
#define FORS(s,i) for(S::iterator i=s.begin(); i!=s.end(); i++)
#define MP make_pair

using namespace std;
long n,k,targetu,targetv,startu,startv,maxX[MAXN],maxY[MAXN],f[MAXN];
pair< pair<long,long>,long> a[MAXN];
S s;

void inp() {
scanf("%ld %ld",&n,&k);
FOR(i,1,n)
scanf("%ld %ld %ld",&a[i].first.first,&a[i].first.second,&a[i].second);
}

void RR() {
//Roi rac hoa theo truc X
FOR(i,1,n)
s.insert(MP(a[i].first.first,i));
long now=s.begin()->first,ind=1;
a[s.begin()->second].first.first=1;
FORS(s,i)
if (i!=s.begin()) {
if (i->first!=now) {
ind++;
now=i->first;
}
a[i->second].first.first=ind;
}
//Roi rac hoa theo truc Y
s.clear();
FOR(i,1,n)
s.insert(MP(a[i].first.second,i));
now=s.begin()->first; ind=1;
a[s.begin()->second].first.second=1;
FORS(s,i)
if (i!=s.begin()) {
if (i->first!=now) {
ind++;
now=i->first;
}
a[i->second].first.second=ind;
}
}

void solve() {
targetu=a[n].first.first;
targetv=a[n].first.second;
startu=a[1].first.first;
startv=a[1].first.second;

sort(a+1,a+n+1);
FOR(i,1,n) {
if (a[i].first.first==startu&&a[i].first.second==startv) {
f[i]=a[i].second;
maxX[a[i].first.first]=f[i];
maxY[a[i].first.second]=f[i];
} else {
long temp=max(maxX[a[i].first.first],maxY[a[i].first.second])-k;
if (temp>=0) temp+=a[i].second; else temp=0;
f[i]=temp;
maxX[a[i].first.first]>?=f[i];
maxY[a[i].first.second]>?=f[i];
}
}
FOR(i,1,n)
if (a[i].first.first==targetu&&a[i].first.second==targetv)
printf("%ld\n",f[i]);
}

int main() {
#ifdef DEBUG
freopen("input.txt","r",stdin);
freopen("output.txt","w",stdout);
#endif
inp();
RR();
solve();
return 0;
}


#### Code mẫu của hieult

#include <set>
#include <map>
#include <list>
#include <cmath>
#include <ctime>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <cctype>
#include <cstdio>
#include <string>
#include <vector>
#include <cassert>
#include <cstdlib>
#include <cstring>
#include <sstream>
#include <iomanip>
#include <iostream>
#include <algorithm>

using namespace std;

typedef long long ll;
typedef long double ld;
typedef unsigned int ui;
typedef unsigned long long ull;

#define Rep(i,n) for(typeof(n) i = 0; i < (n); ++i)
#define Repd(i,n) for(typeof(n) i = (n)-1; i >= 0; --i)
#define For(i,a,b) for(typeof(b) i = (a); i <= (b); ++i)
#define Ford(i,a,b) for(typeof(a) i = (a); i >= (b); --i)
#define Fit(i,v) for(typeof((v).begin()) i = (v).begin(); i != (v).end(); ++i)
#define Fitd(i,v) for(typeof((v).rbegin()) i = (v).rbegin(); i != (v).rend(); ++i)
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define sz(a) ((int)(a).size())
#define all(a) (a).begin(), (a).end()
#define ms(a,x) memset(a, x, sizeof(a))
#define nl puts("")
#define sp printf(" ")
#define ok puts("ok")
//#include <conio.h>

template<class F, class T> T convert(F a, int p = -1) { stringstream ss; if (p >= 0) ss << fixed << setprecision(p); ss << a; T r; ss >> r; return r; }
template<class T> void db(T a, int p = -1) { if (p >= 0) cout << fixed << setprecision(p); cout << a << " "; }
template<class T> T gcd(T a, T b) { T r; while (b != 0) { r = a % b; a = b; b = r; } return a; }
template<class T> T lcm(T a, T b) { return a / gcd(a, b) * b; }
template<class T> T sqr(T x) { return x * x; }
template<class T> T cube(T x) { return x * x * x; }
template<class T> struct Triple { T x, y, z; Triple() {} Triple(T _x, T _y, T _z) : x(_x), y(_y), z(_z) {} };
template<class T> Triple<T> euclid(T a, T b) { if (b == 0) return Triple<T>(1, 0, a); Triple<T> r = euclid(b, a % b); return Triple<T>(r.y, r.x - a / b * r.y, r.z); }
template<class T> int getbit(T s, int i) { return (s >> i) & 1; }
template<class T> T onbit(T s, int i) { return s | (T(1) << i); }
template<class T> T offbit(T s, int i) { return s & (~(T(1) << i)); }
template<class T> int cntbit(T s) { return s == 0 ? 0 : cntbit(s >> 1) + (s & 1); }
const int bfsz = 1 << 16; char bf[bfsz + 5]; int rsz = 0;int ptr = 0;
char gc() { if (rsz <= 0) { ptr = 0; rsz = fread(bf, 1, bfsz, stdin); if (rsz <= 0) return EOF; } --rsz; return bf[ptr++]; }
void ga(char &c) { c = EOF; while (!isalpha(c)) c = gc(); }
int gs(char s[]) { int l = 0; char c = gc(); while (isspace(c)) c = gc(); while (c != EOF && !isspace(c)) { s[l++] = c; c = gc(); } s[l] = '\0'; return l; }
template<class T> bool gi(T &v) {
v = 0; char c = gc(); while (c != EOF && c != '-' && !isdigit(c)) c = gc(); if (c == EOF) return false; bool neg = c == '-'; if (neg) c = gc();
while (isdigit(c)) { v = v * 10 + c - '0'; c = gc(); } if (neg) v = -v; return true;
}

const double PI = 2 * acos(0);
const string months[] = {"January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"};
const int days[] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
const int dr[] = {-1, 0, +1, 0};
const int dc[] = {0, +1, 0, -1};
const int inf = (int)1e9 + 5;
const ll linf = (ll)1e16 + 5;
const double eps = 1e-9;
const ll mod = 100000007;
typedef pair<int, int> II;

#define maxn 300005

pair<II, II> A[maxn];
int n, k, fx[maxn], fy[maxn], f[maxn];

int main() {
//    freopen("in.txt", "r", stdin);
//    freopen("out.txt", "w", stdout);
ms(f, -1); ms(fx, -1); ms(fy, -1);
gi(n); gi(k);
Rep(i, n){
gi(A[i].fi.fi); gi(A[i].fi.se); gi(A[i].se.fi);
A[i].se.se = i + 1;
}
sort(A, A + n);
bool flag = false;
int x, y, num, id, t;
Rep(i, n){

if(!flag && A[i].se.se != 1) continue;
x = A[i].fi.fi; y = A[i].fi.se; num = A[i].se.fi; id = A[i].se.se;
if(A[i].se.se == 1){
flag = true;
fx[x] = max(fx[x], num);
fy[y] = max(fy[y], num);
continue;
}
t = max(fx[x], fy[y]);
if(t < k) continue;
fx[x] = max(fx[x], t - k + num);
fy[y] = max(fy[y], t - k + num);
if(id == n){
printf("%d", t - k + num);
return 0;
}
}
}


#### Code mẫu của ll931110

{\$MODE DELPHI}
program BARICAVN;
uses math;
const
input  = '';
output = '';
maxn = 300000;
maxt = 100000;
type
rec = record
x,y,val,pos: integer;
end;
var
a: array[1..maxn] of rec;
maxx,maxy: array[0..maxt] of integer;
n,k: integer;

procedure init;
var
f: text;
i: integer;
begin
assign(f, input);
reset(f);

for i := 1 to n do
begin
a[i].pos := i;
end;

close(f);
end;

procedure swap(var u,v: rec);
var
z: rec;
begin
z := u;  u := v;  v := z;
end;

function lower(u,v: rec): boolean;
begin
lower := (u.x < v.x) or ((u.x = v.x) and (u.y < v.y));
end;

procedure quicksort;

procedure par(l,h: integer);
var
i,j: integer;
p: rec;
begin
if l >= h then exit;
i := l; j := h; p := a[random(h - l + 1) + l];

repeat
while lower(a[i],p) do inc(i);
while lower(p,a[j]) do dec(j);

if i <= j then
begin
if i < j then swap(a[i],a[j]);
inc(i);
dec(j);
end;
until i > j;

par(l,j);
par(i,h);
end;

begin
par(1,n);
end;

procedure solve;
var
f: text;
i,t: integer;
begin
for i := 0 to maxt do
begin
maxx[i] := -maxn;
maxy[i] := -maxn;
end;

i := 1;
while a[i].pos <> 1 do inc(i);
maxx[a[i].x] := a[i].val;
maxy[a[i].y] := a[i].val;

repeat
inc(i);
t := max(maxx[a[i].x],maxy[a[i].y]);
if t >= k then t := t - k + a[i].val;
if maxx[a[i].x] < t then maxx[a[i].x] := t;
if maxy[a[i].y] < t then maxy[a[i].y] := t;
until a[i].pos = n;

assign(f, output);
rewrite(f);
writeln(f, t);
close(f);
end;

begin
init;
quicksort;
solve;
end.