#include "circus.h"
#include<bits/stdc++.h>
using namespace std;
#define fast ios::sync_with_stdio(false); cin.tie(0);
#define fi first
#define se second
#define em emplace
#define eb emplace_back
#define all(v) (v).begin(), (v).end()
#define mp make_pair
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef pair<int,pii> piii;
const int inf = 1e9;
const ll INF = 1e18;
int n, m;
int dp[100010];
bool chk[100010];
vector<int> p;
priority_queue<piii, vector<piii>, greater<piii>> pQ;
int Min[400010];
int Max[400010];
void update(int node, int s, int e, int i, int x) {
if(s == e){
Min[node] = min(Min[node], x);
Max[node] = max(Max[node], x);
return;
}
int m = s + e >> 1;
if(i <= m) update(node*2, s, m, i, x);
else update(node*2+1, m+1, e, i, x);
Min[node] = min(Min[node*2], Min[node*2+1]);
Max[node] = max(Max[node*2], Max[node*2+1]);
}
int mx(int node, int s, int e, int l, int r) {
if(r < s || e < l) return 0;
if(l <= s && e <= r) return Max[node];
return max(mx(node*2, s, (s+e)/2, l, r), mx(node*2+1, (s+e)/2+1, e, l, r));
}
int mn(int node, int s, int e, int l, int r) {
if(r < s || e < l) return 0;
if(l <= s && e <= r) return Min[node];
return min(mn(node*2, s, (s+e)/2, l, r), mn(node*2+1, (s+e)/2+1, e, l, r));
}
void init(int N, int M, int P[]){
n = N;
m = M;
for(int i=0; i<n; i++) p.eb(P[i]);
p.eb(0);
p.eb(m);
sort(all(p));
p.erase(unique(all(p)), p.end());
pQ.em(0, mp(p.size()-1, p.size()-1));
while(pQ.size()) {
int cost = pQ.top().fi;
int x = pQ.top().se.fi;
int par = pQ.top().se.se;
pQ.pop();
if(x >= par && x+1 < p.size()) pQ.em(p[x+1] - p[par], mp(x+1, par));
else if(x <= par && x-1 >= 0) pQ.em(p[par] - p[x-1], mp(x-1, par));
if(chk[x]) continue;
chk[x] = true;
dp[x] = cost;
int k = lower_bound(all(p), p[x] + cost) - p.begin();
if(k < p.size()) pQ.em(p[k] - p[x], mp(k, x));
k = upper_bound(all(p), p[x] - cost) - p.begin() - 1;
if(k >= 0) pQ.em(p[x] - p[k], mp(k, x));
}
for(int i=0; i<p.size(); i++) {
if(p[i] - dp[i] >= 0) update(1, 0, m, p[i] - dp[i], p[i]);
if(p[i] + dp[i] <= m) update(1, 0, m, p[i] + dp[i], p[i]);
}
}
int minLength(int D) {
int ret = m - D;
ret = min(ret, mx(1, 0, m, D, m) - D);
ret = min(ret, D + mn(1, 0, m, 0, D));
return ret;
}
