#include "circus.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
const int MAXN = 3e5;
const int INF = 1e9+100;
int N, M, P[MAXN+10];
int dist[MAXN+10];
struct Queue
{
int u, w;
bool operator < (const Queue &p) const { return w>p.w; }
};
struct BIT
{
int tree[MAXN+10];
void init() { for(int i=1; i<=N; i++) tree[i]=INF; }
void update(int i, int k) { for(; i<=N; i+=(i&-i)) tree[i]=min(tree[i], k); }
int query(int i) { int ret=INF; for(; i>0; i-=(i&-i)) ret=min(ret, tree[i]); return ret; }
};
BIT bit1, bit2;
vector<int> comp1, comp2;
void init(int _N, int _M, int _P[])
{
N=_N; M=_M;
for(int i=1; i<=N; i++) P[i]=_P[i-1];
sort(P+1, P+N+1);
N=unique(P+1, P+N+1)-P-1;
P[0]=M;
for(int i=0; i<=3*N; i++) dist[i]=INF;
priority_queue<Queue> PQ;
PQ.push({2*N, M-P[N]}); dist[0]=0;
while(!PQ.empty())
{
Queue now=PQ.top(); PQ.pop();
if(dist[now.u]<=now.w) continue;
dist[now.u]=now.w;
if(now.u<=N)
{
int t=upper_bound(P+1, P+N+1, P[now.u]-now.w)-P-1;
if(t!=0) PQ.push({N+t, P[now.u]-P[t]});
t=lower_bound(P+1, P+N+1, P[now.u]+now.w)-P;
if(t!=N+1) PQ.push({N*2+t, P[t]-P[now.u]});
}
else if(now.u<=2*N)
{
PQ.push({now.u-N, now.w});
if(now.u!=N+1) PQ.push({now.u-1, now.w+P[now.u-N]-P[now.u-N-1]});
}
else
{
PQ.push({now.u-2*N, now.w});
if(now.u!=3*N) PQ.push({now.u+1, now.w+P[now.u+1-2*N]-P[now.u-2*N]});
}
}
//for(int i=1; i<=N; i++) printf("%d ", dist[i]); printf("\n");
bit1.init(); bit2.init();
for(int i=1; i<=N; i++) comp1.push_back(P[i]+dist[i]);
sort(comp1.begin(), comp1.end());
comp1.erase(unique(comp1.begin(), comp1.end()), comp1.end());
for(int i=1; i<=N; i++) comp2.push_back(P[i]-dist[i]);
sort(comp2.begin(), comp2.end());
comp2.erase(unique(comp2.begin(), comp2.end()), comp2.end());
for(int i=1; i<=N; i++)
{
int p=lower_bound(comp1.begin(), comp1.end(), P[i]+dist[i])-comp1.begin()+1;
bit1.update(p, -P[i]);
}
for(int i=1; i<=N; i++)
{
int p=lower_bound(comp2.begin(), comp2.end(), P[i]-dist[i])-comp2.begin()+1;
bit2.update(N-p+1, P[i]);
}
}
int minLength(int D)
{
int ans=M-D;
int p=upper_bound(comp1.begin(), comp1.end(), D)-comp1.begin();
ans=min(ans, D+bit1.query(p));
p=lower_bound(comp2.begin(), comp2.end(), D)-comp2.begin()+1;
ans=min(ans, bit2.query(N-p+1)-D);
return ans;
}
