#include <bits/stdc++.h>
int32_t main() {
std::ios_base::sync_with_stdio(false);
std::cin.tie(nullptr);
int n, k, x;
std::cin >> n >> k >> x;
std::vector<std::array<int, 3>> input(n);
for (auto& [l, t, r] : input) {
std::cin >> l >> t >> r;
r++;
}
std::vector<int> all;
for (auto& [l, t, r] : input) {
all.push_back(l);
all.push_back(l + std::min(t, r - l));
all.push_back(r);
}
std::sort(all.begin(), all.end());
all.erase(std::unique(all.begin(), all.end()), all.end());
int m = all.size() - 1;
std::vector<int> cnt(m + 1), cnt_ch(m + 1);
for (auto [l, t, r] : input) {
int lc = l + std::min(t, r - l);
int it1 = std::lower_bound(all.begin(), all.end(), l) - all.begin();
int it2 = std::lower_bound(all.begin(), all.end(), lc) - all.begin();
int it3 = std::lower_bound(all.begin(), all.end(), r) - all.begin();
cnt[it1]++;
cnt[it3]--;
cnt_ch[it2]++;
cnt_ch[it3]--;
}
for (int i = 0, c1 = 0, c2 = 0; i < m; i++) {
c1 += cnt[i];
cnt[i] = c1;
c2 += cnt_ch[i];
cnt_ch[i] = c2;
cnt_ch[i] *= cnt[i] >= k;
}
std::vector<int64_t> prf(m + 1);
for (int i = 0; i < m; i++) {
prf[i + 1] = prf[i] + cnt_ch[i] * int64_t(all[i + 1] - all[i]);
}
int64_t ans = 0;
auto get_prf = [&](int p) {
p = std::max(p, all[0]);
auto it = std::upper_bound(all.begin(), all.end(), p) - all.begin();
return prf[it - 1] + cnt_ch[it - 1] * int64_t(p - all[it - 1]);
};
auto upd = [&](int l, int r) {
int64_t res = get_prf(r) - get_prf(l);
ans = std::max(ans, res);
};
for (int i = 0; i <= m; i++) {
upd(all[i], all[i] + x);
upd(all[i] - x, all[i]);
}
std::cout << ans << "\n";
return 0;
}
