#include <bits/stdc++.h>
typedef long long ll;
using namespace std;
struct Event{
int t, typ, i; ///0 -> on, 1 -> off, 2 -> extra on, 3 -> extra off
Event(){}
Event(int _t, int _typ, int _i): t(_t), typ(_typ), i(_i) {}
bool operator < (const Event &E) const{return t < E.t;}
};
struct Foo{
int t, c;
ll S;
Foo(){}
Foo(int _t): t(_t) {c = 0; S = 0;}
bool operator < (const Foo &F) const{return t < F.t;}
};
vector<Event> E;
vector<Foo> F;
int _on1[100100], _on2[100100], cnt1, cnt2;
void on1(int x){
assert(_on1[x]==0);
_on1[x] = 1;
cnt1++;
}
void off1(int x){
assert(_on1[x]==1);
_on1[x] = 0;
cnt1--;
}
void on2(int x){
assert(_on2[x]==0);
_on2[x] = 1;
cnt2++;
}
void off2(int x){
assert(_on2[x]==1);
_on2[x] = 0;
cnt2--;
}
int main(){
int n, k, x;
scanf("%d %d %d", &n, &k, &x);
for (int i=1;i<=n;i++){
int l, t, r;
scanf("%d %d %d", &l, &t, &r);
E.emplace_back(l, 0, i);
E.emplace_back(r+1, 1, i);
if (l+t <= r){
E.emplace_back(l+t, 2, i);
E.emplace_back(r+1, 3, i);
}
}
sort(E.begin(), E.end());
F.emplace_back(0);
for (int i=0;i<(int)E.size();){
int r = i;
while(r<(int)E.size() && E[i].t == E[r].t){
if (E[r].typ==0) on1(E[r].i);
else if (E[r].typ==1) off1(E[r].i);
else if (E[r].typ==2) on2(E[r].i);
else off2(E[r].i);
++r;
}
F.emplace_back(E[i].t);
//printf(" t = %d: on: %d / extra: %d / k: %d\n", E[i].t, cnt1, cnt2, k);
if (cnt1 >= k) F.back().c = cnt2;
i = r;
}
for (int i=1;i<(int)F.size()-1;i++){
F[i].S = F[i-1].S + (ll)F[i].c * (F[i+1].t - F[i].t);
}
//for (auto &[t, c, S]:F) printf(" %d %d %lld\n", t, c, S);
ll ans = 0;
for (int s=1;s<(int)F.size();s++){
auto iter = --lower_bound(F.begin(), F.end(), Foo(F[s].t + x));
if (iter==F.begin()) continue;
ll val = prev(iter)->S - F[s-1].S;
//printf(" %lld\n", val);
val += (ll)(iter->c) * (F[s].t + x - (iter->t));
ans = max(ans, val);
//printf("start %d -> %lld\n", F[s].t, val);
}
for (int e=(int)F.size()-1;e;e--){
auto iter = lower_bound(F.begin(), F.end(), Foo(F[e].t - x));
if (iter==F.begin()) {ans = max(ans, F[e-1].S); continue;}
ll val = F[e-1].S - prev(iter)->S;
val += (ll)(prev(iter)->c) * (iter->t - (F[e].t-x));
ans = max(ans, val);
//printf("end %d -> %lld\n", F[e].t, val);
}
printf("%lld\n", ans);
return 0;
}
