#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include "lottery.h"
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
//mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
//ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
struct node
{
int l = 0;
int r = (1LL<<31LL)-1;
int cnt = 0;
ll sum = 0;
node* left = NULL;
node* right = NULL;
void sons()
{
if(left == NULL)
{
left = new node;
left -> l = l;
left -> r = ((ll)l+r)/2;
right = new node;
right -> l = ((ll)l+r)/2+1;
right -> r = r;
}
}
void add_num(ll x,node* prev)
{
cnt = prev->cnt+1;
sum = prev->sum+x;
if(l==r) return;
prev->sons();
if(x <= ((ll)l+r)/2)
{
right = prev->right;
left = new node;
left -> l = l;
left -> r = ((ll)l+r)/2;
left -> add_num(x,prev->left);
}
else
{
left = prev->left;
right = new node;
right -> l = ((ll)l+r)/2+1;
right -> r = r;
right -> add_num(x,prev->right);
}
}
};
const int tree_siz = 1024*512-1;
int min_[tree_siz+1];
int get_min(int akt, int p1, int p2, int s1, int s2)
{
if(p2 < s1 || p1 > s2) return 2e9;
if(p1 >= s1 && p2 <= s2) return min_[akt];
return min(get_min(akt*2,p1,(p1+p2)/2,s1,s2),get_min(akt*2+1,(p1+p2)/2+1,p2,s1,s2));
}
void upd(int v, int m)
{
min_[v] = min(min_[v],m);
if(v != 1) upd(v/2,m);
}
vector<node> Xtree;
vector<node> Ytree;
bool check(ll Xless_sum, ll Yless_sum, int Xless, int Yless, int len, int mn, ll ans)
{
if(ans > mn) return 0;
ll sum = len*ans/2;
return ans*Yless-Yless_sum <= sum && Xless_sum + (len-Xless)*ans >= sum;
}
int get_ans(int p1, int p2, node* Xbeg, node* Xend, node* Ybeg, node* Yend, int mn, int len, ll Xless_sum = 0, ll Yless_sum = 0, int Xless = 0, int Yless = 0)
{
if(p1 == p2) return p1-1;
int ans = ((ll)p1+p2)/2;
Xbeg->sons();
Ybeg->sons();
Xend->sons();
Yend->sons();
Xless_sum += Xend->left->sum-Xbeg->left->sum;
Yless_sum += Yend->left->sum-Ybeg->left->sum;
Xless += Xend->left->cnt-Xbeg->left->cnt;
Yless += Yend->left->cnt-Ybeg->left->cnt;
if(check(Xless_sum,Yless_sum,Xless,Yless,len,mn,ans)) return get_ans(ans+1,p2,Xbeg->right,Xend->right,Ybeg->right,Yend->right,mn,len,Xless_sum,Yless_sum,Xless,Yless);
Xless_sum -= Xend->left->sum-Xbeg->left->sum;
Yless_sum -= Yend->left->sum-Ybeg->left->sum;
Xless -= Xend->left->cnt-Xbeg->left->cnt;
Yless -= Yend->left->cnt-Ybeg->left->cnt;
return get_ans(p1,ans,Xbeg->left,Xend->left,Ybeg->left,Yend->left,mn,len,Xless_sum,Yless_sum,Xless,Yless);
}
void init(int n, int q, vi X, vi Y)
{
Xtree.pb(node());
Ytree.pb(node());
rep(i,tree_siz+1) min_[i] = 2e9;
rep(i,n)
{
upd((tree_siz/2+2+i),X[i]+Y[i]);
}
rep(i,n)
{
node pom;
pom.add_num(X[i],&Xtree.back());
Xtree.pb(pom);
}
rep(i,n)
{
node pom;
pom.add_num(Y[i],&Ytree.back());
Ytree.pb(pom);
}
}
int max_prize(int L, int R)
{
L++;
R++;
return get_ans(0,(1LL<<31LL)-1,&Xtree[L-1],&Xtree[R],&Ytree[L-1],&Ytree[R],get_min(1,0,tree_siz/2,L,R),R-L+1);
}
