#include "shortcut.h"
#include<stdio.h>
#include<algorithm>
#include<vector>
#define N_ 1010000
#define SZ 1048576
#define pll pair<long long, long long>
using namespace std;
int n;
long long LD[N_], RD[N_], S[N_], P[N_], IT1[SZ+SZ], IT2[SZ+SZ], TL;
long long LT[N_], RT[N_];
int RR[N_], LL[N_];
long long Max1(int b, int e){
long long r = -1e18;
b+=SZ;e+=SZ;
while(b<=e){
r=max(r,max(IT1[b],IT1[e]));
b=(b+1)>>1,e=(e-1)>>1;
}
return r;
}
long long Max2(int b, int e){
long long r = -1e18;
b+=SZ,e+=SZ;
while(b<=e){
r=max(r,max(IT2[b],IT2[e]));
b=(b+1)>>1,e=(e-1)>>1;
}
return r;
}
long long st[1010000][2];
bool Pos(long long d){
if(LD[n]<=d)return true;
int i, pv = n, ppv = 1;
long long Mx = 0;
for(i=1;i<=n;i++){
if(LD[i] > d){RR[i]=-1;continue;}
if(i!=1){
while(1){
long long Len = S[pv]-S[i]+TL, mm;
if(ppv < i)ppv = i;
if(ppv > pv)ppv = pv;
while((S[ppv+1]-S[i])*2 <= Len && ppv+1<=pv) ppv++;
while((S[ppv]-S[i])*2 > Len)ppv--;
mm = Max1(i,ppv) + Mx;
if(ppv<pv) mm = max(mm,Max2(ppv+1,pv) + Mx + S[pv]+S[i]+TL);
if(mm > d) pv--;
else break;
}
}
RR[i] = pv;
Mx = max(Mx, P[i]-S[i]);
}
Mx = 0, pv = 1, ppv = n;
for(i=n;i>=1;i--){
if(RD[i] > d){LL[i]=-1;continue;}
if(i!=n){
while(1){
long long Len = S[i]-S[pv]+TL, mm;
if(ppv > i)ppv = i;
if(ppv < pv)ppv = pv;
while((S[i]-S[ppv-1])*2 <= Len && ppv-1>=pv) ppv--;
while((S[i]-S[ppv])*2 > Len)ppv++;
mm = Max2(ppv,i) + Mx;
if(ppv>pv) mm = max(mm,Max1(pv,ppv-1) + Mx - S[pv]-S[i]+TL);
if(mm > d) pv++;
else break;
}
}
LL[i] = pv;
Mx = max(Mx, P[i]+S[i]);
}
long long ML = 1e18;
int top = 0;
for(i=1;i<=n;i++){
if(top && st[1][0] + P[i] + S[i] > d){
int bb = 1, ee = top, rr=0, mid;
while(bb<=ee){
mid=(bb+ee)>>1;
if(st[mid][0]+P[i]+S[i]>d){
rr = mid;
bb = mid + 1;
}
else ee = mid-1;
}
ML = min(ML, d - (st[rr][1] + P[i] - S[i]));
}
while(top && P[i]-S[i] >= st[top][0])top--;
top++;
st[top][0]=P[i]-S[i];
st[top][1]=P[i]+S[i];
}
pv = 1;
for(i=1;i<n;i++){
pv=max(pv,i);
while(pv+1<=n && S[pv+1]-S[i]+TL <=ML)pv++;
int t = min(pv, RR[i]);
if(t <= i || LL[t]==-1)continue;
if(LL[t] > i)continue;
if(LT[i] + RT[t] - (S[t]-S[i]) + TL <= d)return true;
}
return false;
}
long long find_shortcut(int N, vector<int> l, vector<int> d, int c)
{
TL = c;
n = N;
int i;
for(i=1;i<=n;i++){
if(i!=1)S[i] = S[i-1] + l[i-2];
P[i] = d[i-1];
}
long long mx = 0;
for(i=1;i<=n;i++){
LD[i] = max(LD[i-1], mx+S[i]+P[i]);
mx = max(mx, P[i]-S[i]);
LT[i] = mx;
}
mx = S[n];
for(i=n;i>=1;i--){
RD[i] = max(RD[i+1], mx-S[i]+P[i]);
mx = max(mx, P[i]+S[i]);
RT[i] = mx;
int t = i+SZ;
IT1[t] = S[i]+P[i], IT2[t] = P[i]-S[i];
while(t!=1){
t>>=1;
IT1[t] = max(IT1[t+t],IT1[t+t+1]);
IT2[t] = max(IT2[t+t],IT2[t+t+1]);
}
}
long long b = 0, e = LD[n], mid, res = 0;
while(b<=e){
mid = (b+e)/2;
if(Pos(mid)){
res = mid;
e = mid - 1;
}
else b = mid + 1;
}
return res;
}
