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| #include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define MOD 1000000007
#define rep(i, a, n) for (ll i = a; i < n; i++)
#define pb push_back
#define SEG_ROOT 1,0,n-1
#define SEG_L o<<1,l,m
#define SEG_R o<<1|1,m+1,r
const double pi = acos(-1.0);
const int N = 500'000;
ll s[N + 10];
ll t[N + 10];
ll dp[N + 10];
ll a[3][N + 10];
vector<tuple<int, int, ll> > rlv;
ll seg[2][N * 4 + 10];
ll segans[N * 4 + 10];
const ll INF = 0x3f3f3f3f3f3f3f3f;
ll query(int o, int l, int r, int ql, int qr) {
if (l == ql && r == qr)
return seg[0][o];
int m = (l + r) / 2;
if (qr <= m) {
return query(SEG_L, ql, qr);
} else if (ql > m) {
return query(SEG_R, ql, qr);
} else {
return max(query(SEG_L, ql, m),
query(SEG_R, m + 1, qr));
}
}
void update(int o, int l, int r, int pos) {
if (l == r) {
seg[0][o] = dp[l];
return;
}
int m = (l + r) / 2;
if (pos <= m)
update(SEG_L, pos);
else
update(SEG_R, pos);
seg[0][o] = max(seg[0][o << 1], seg[0][o << 1 | 1]);
}
void build(int o, int l, int r) {
if (l == r) {
seg[0][o] = dp[l];
return;
}
int m = (l + r) / 2;
build(SEG_L);
build(SEG_R);
seg[0][o] = max(seg[0][o << 1], seg[0][o << 1 | 1]);
}
void buildans(int o, int l, int r) {
if (l == r) {
seg[0][o] = max(max(dp[l], s[l]), l > 0 ? dp[l-1] : -INF);
seg[1][o] = t[l];
segans[o] = seg[0][o] + t[l];
return;
}
int m = (l + r) / 2;
buildans(SEG_L);
buildans(SEG_R);
seg[0][o] = max(seg[0][o << 1], seg[0][o << 1 | 1]);
seg[1][o] = max(seg[1][o << 1], seg[1][o << 1 | 1]);
segans[o] = max(seg[0][o << 1] + seg[1][o << 1 | 1],
max(segans[o << 1], segans[o << 1 | 1]));
};
vector<ll> qans(int o, int l, int r, int ql, int qr) {
if (ql == l && qr == r) {
return {segans[o], seg[0][o], seg[1][o]};
}
int m = (l + r) / 2;
if (qr <= m) {
return qans(SEG_L, ql, qr);
} else if (ql > m) {
return qans(SEG_R, ql, qr);
}
auto lres = qans(SEG_L, ql, m);
auto rres = qans(SEG_R, m + 1, qr);
return {max(max(lres[0], rres[0]), lres[1] + rres[2]), max(lres[1], rres[1]),
max(lres[2], rres[2])};
}
int main() {
int n, q;
scanf("%d %d", &n, &q);
ll a2 = 0;
rep(i, 0, 3) {
rep(j, 0, n) { scanf("%lld", &a[i][j]); }
}
rep(i, 0, n) a2 += a[2][i];
s[0] = a[0][0];
rep(i, 1, n) { s[i] = s[i - 1] + a[0][i] - a[1][i - 1]; }
t[0] = a2 + a[1][0];
rep(i, 1, n) { t[i] = t[i - 1] + a[1][i] - a[2][i - 1]; }
rep(i, 0, q) {
int r, l;
ll v;
scanf("%d %d %lld", &l, &r, &v);
rlv.pb({r - 1, l - 1, v});
}
ll ans = -INF;
sort(rlv.begin(), rlv.end());
vector<int> pos;
unsigned long itr = 0;
rep(i, 0, n){
dp[i] = -INF;
}
rep(i, 0, n) {
while (pos.size() && s[pos.back()] <= s[i]) {
pos.pop_back();
}
pos.pb(i);
while (itr < rlv.size() && get<0>(rlv[itr]) == i) {
dp[i] = max(
dp[i],
s[*lower_bound(pos.begin(), pos.end(), get<1>(rlv[itr]))] -
get<2>(rlv[itr]));
if (dp[i] != -INF) {
ans = max(ans, dp[i] + t[i]);
}
itr++;
}
}
build(SEG_ROOT);
itr = 0;
for(auto [r,l,v]:rlv){
ll newdpi = query(SEG_ROOT, max(0,l-1), max(0,r-1)) - v;
if (newdpi > dp[r]) {
dp[r] = newdpi;
ans = max(ans, dp[r] + t[r]);
update(SEG_ROOT, r);
}
}
buildans(SEG_ROOT);
for (auto [r, l, v] : rlv) {
auto qres = qans(SEG_ROOT, l, r);
if (qres[0] <= -INF)
continue;
ans = max(ans, qres[0] - v);
}
printf("%lld\n", ans);
return 0;
}
|