#include "circus.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ld long double
#define ar array
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template <typename T> using oset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#define vt vector
#define eb emplace_back
#define pb push_back
#define rsz resize
#define asn assign
#define all(c) (c).begin(), (c).end()
#define sz(x) (int)(x).size()
#define pll pair<ll, ll>
#define pii pair<int, int>
#define f first
#define s second
#define F_OR(i, a, b, s) for (int i=(a); (s)>0?i<(b):i>(b); i+=(s))
#define F_OR1(e) F_OR(i, 0, e, 1)
#define F_OR2(i, e) F_OR(i, 0, e, 1)
#define F_OR3(i, b, e) F_OR(i, b, e, 1)
#define F_OR4(i, b, e, s) F_OR(i, b, e, s)
#define GET5(a, b, c, d, e, ...) e
#define F_ORC(...) GET5(__VA_ARGS__, F_OR4, F_OR3, F_OR2, F_OR1)
#define FOR(...) F_ORC(__VA_ARGS__)(__VA_ARGS__)
#define EACH(x, a) for (auto& x: a)
template<class T> bool umin(T& a, const T& b) {
return b<a?a=b, 1:0;
}
template<class T> bool umax(T& a, const T& b) {
return a<b?a=b, 1:0;
}
ll FIRSTTRUE(function<bool(ll)> f, ll lb, ll rb) {
while(lb<rb) {
ll mb=(lb+rb)/2;
f(mb)?rb=mb:lb=mb+1;
}
return lb;
}
ll LASTTRUE(function<bool(ll)> f, ll lb, ll rb) {
while(lb<rb) {
ll mb=(lb+rb+1)/2;
f(mb)?lb=mb:rb=mb-1;
}
return lb;
}
template<class A> void read(vt<A>& v);
template<class A, size_t S> void read(ar<A, S>& a);
template<class A, class B> void read(pair<A, B>& x);
template<class T> void read(T& x) {
cin >> x;
}
void read(double& d) {
string t;
read(t);
d=stod(t);
}
void read(long double& d) {
string t;
read(t);
d=stold(t);
}
template<class H, class... T> void read(H& h, T&... t) {
read(h);
read(t...);
}
template<class A> void read(vt<A>& x) {
EACH(a, x)
read(a);
}
template<class A, size_t S> void read(array<A, S>& x) {
EACH(a, x)
read(a);
}
template<class A, class B> void read(pair<A, B>& x) {
cin >> x.first >> x.second;
}
string to_string(char c) {
return string(1, c);
}
string to_string(bool b) {
return b?"true":"false";
}
string to_string(const char* s) {
return string(s);
}
string to_string(string s) {
return s;
}
string to_string(vt<bool> v) {
string res;
FOR(sz(v))
res+=char('0'+v[i]);
return res;
}
template<size_t S> string to_string(bitset<S> b) {
string res;
FOR(S)
res+=char('0'+b[i]);
return res;
}
template<class T> string to_string(T v) {
bool f=1;
string res;
EACH(x, v) {
if(!f)
res+=' ';
f=0;
res+=to_string(x);
}
return res;
}
template<class A, class B> string to_string(pair<A, B>& x) {
return to_string(x.first) + ' ' + to_string(x.second);
}
template<class A> void write(A x) {
cout << to_string(x);
}
template<class H, class... T> void write(const H& h, const T&... t) {
write(h);
write(t...);
}
void print() {
write("\n");
}
template<class H, class... T> void print(const H& h, const T&... t) {
write(h);
if(sizeof...(t))
write(' ');
print(t...);
}
vt<pii> v;
void init(int n, int m, int p[]){
sort(p, p+n, greater<int>());
v.eb(m, m);
FOR(n) {
auto it=upper_bound(all(v), make_pair(p[i], -1), greater<pii>());
int len=(prev(it)->s)-p[i];
int nx=p[i]-len;
while (nx>=v.back().f) v.pop_back();
v.eb(nx, p[i]);
}
}
int minLength(int d) {
auto it=upper_bound(all(v), make_pair(d, -1), greater<pii>());
int len=(prev(it)->s)-d;
return len;
}
