This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define pb push_back
#define FIO ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
using namespace std;
typedef long long ll;
typedef pair <ll, ll> pii;
const int N = 2e5 + 7;
int n, m;
ll a[N], l[N], r[N], c[N], ps[N];
vector <pii> iv[N];
map <ll, ll> s;
bool check(int t, ll b, ll d) {
if (d > b || d < 0) return 0;
s.clear();
for (int i = 0; i <= n; i++) ps[i] = 0;
ll cnt = 0;
for (int i = 1; i <= t; i++) {
ll ne = (a[i]-b+d+1)/2;
for (auto it : iv[i]) if (it.F >= t) s[it.F] += it.S;
while (cnt < ne) {
if (s.empty()) return 0;
auto p = --s.end();
ll dod = ne-cnt;
if (p->S <= ne-cnt) {
dod = p->S;
s.erase(p);
}
else s[p->F] -= dod;
cnt += dod;
ps[0] += dod;
ps[i] -= 2*dod;
ps[p->F+1] += 2*dod;
}
}
for (int i = 0; i < n; i++) {
if (i) ps[i] += ps[i-1];
if (a[i] + ps[i] > b) return 0;
}
return 1;
}
int main () {
FIO;
cin >> n >> m;
for (int i = 0; i < m; i++) {
cin >> l[i] >> r[i] >> c[i];
if (l[i] > r[i]) swap(l[i], r[i]);
r[i]--;
a[l[i]] += c[i];
a[r[i]+1] -= c[i];
iv[l[i]].pb({r[i], c[i]});
}
for (int i = 1; i < n; i++) a[i] += a[i-1];
int p = 1;
for (int i = 2; i < n; i++) if (a[i] > a[p]) p = i;
ll lo = 0, hi = a[p];
while (lo < hi) {
ll mid = (lo + hi) / 2;
int o = 0;
o |= check(p, mid, a[p]-mid) | check(p, mid, a[p]-mid+1);
if (o) hi = mid;
else lo = mid+1;
}
cout << lo << "\n";
return 0;
}
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