/*
*/

//#pragma GCC optimize("O3")
#define _CRT_SECURE_NO_WARNINGS
#include <fstream>
#include <iostream>
#include <string>
#include <complex>
#include <math.h>
#include <set>
#include <vector>
#include <map>
#include <queue>
#include <stdio.h>
#include <stack>
#include <algorithm>
#include <list>
#include <ctime>

#include <memory.h>
#include <assert.h>

#define y0 sdkfaslhagaklsldk

#define y1 aasdfasdfasdf
#define yn askfhwqriuperikldjk
#define j1 assdgsdgasghsf
#define tm sdfjahlfasfh
#define lr asgasgash
#define norm asdfasdgasdgsd
#define have adsgagshdshfhds
#define ends asdgahhfdsfshdshfd

#define eps 1e-8
#define M_PI 3.141592653589793
#define bsize 512

#define ldouble long double
using namespace std;

#define bs 1000000007

const int N = 2000031;

int n,k;
int A[N];
vector<pair<int,int> > mins,maxs;
long long t[N*4],toadd[N*4];

int first_present[N],first_absent[N];
int ar[N];

long long t_max[N*4],toadd_max[N*4];

void push(int v){
	t[v*2]+=toadd[v];
	toadd[v*2]+=toadd[v];
	t[v*2+1]+=toadd[v];
	toadd[v*2+1]+=toadd[v];
	toadd[v]=0;
}

int get(int v,int tl,int tr){
	if (tl==tr)
		return tl;
	push(v);
	int tm=tl+tr;
	tm/=2;
	if (t[v*2+1]>=k)
		return get(v*2+1,tm+1,tr);
	return get(v*2,tl,tm);
}

void add(int v,int tl,int tr,int l,int r,int val){
	if (l>r)
		return;
	if (tl==l&&tr==r){
		t[v]+=val;
		toadd[v]+=val;
		return;
	}
	push(v);
	int tm=tl+tr;
	tm/=2;
	add(v*2,tl,tm,l,min(r,tm),val);
	add(v*2+1,tm+1,tr,max(tm+1,l),r,val);
	t[v]=max(t[v*2],t[v*2+1]);
}

void UPD(int l,int r,int val){
	add(1,1,n,l,r,val);
}

int get_rmost(){
	if (t[1]<k)
		return -123;
	return get(1,1,n);
}

void push_max(int v){
	toadd_max[v*2]=max(toadd_max[v*2],toadd_max[v]);
	t_max[v*2]=max(t_max[v*2],toadd_max[v]);
	toadd_max[v*2+1]=max(toadd_max[v*2+1],toadd_max[v]);
	t_max[v*2+1]=max(t_max[v*2+1],toadd_max[v]);
	toadd_max[v]=-2e9;
}

void update(int v,int tl,int tr,int l,int r,long long val){
	if (l>r)
		return;
	if (tl==l&&tr==r){
		t_max[v]=max(t_max[v],val);
		toadd_max[v]=max(toadd_max[v],val);
		return;
	}
	push_max(v);
	int tm=tl+tr;
	tm/=2;
	update(v*2,tl,tm,l,min(r,tm),val);
	update(v*2+1,tm+1,tr,max(tm+1,l),r,val);
	t_max[v]=max(t_max[v*2],t_max[v*2+1]);
}

long long get(int v,int tl,int tr,int ps)
{
	if (tl==tr){
		return t_max[v];
	}
	push_max(v);
	int tm=tl+tr;
	tm/=2;
	if (ps<=tm)
		return get(v*2,tl,tm,ps);
	else
		return get(v*2+1,tm+1,tr,ps);
}

void Build(int v,int tl,int tr){
	t_max[v]=-1;
	toadd_max[v]=-1e9;
	if (tl==tr)
		return;
	int tm=tl+tr;
	tm/=2;
	Build(v*2,tl,tm);
	Build(v*2+1,tm+1,tr);
}

int main(){
//	freopen("apache.in","r",stdin);
//	freopen("apache.out","w",stdout);
	//freopen("input.txt", "r", stdin);
	//freopen("output.txt", "w", stdout);
	ios_base::sync_with_stdio(0);
//	cin.tie(0);

	cin>>n>>k;
	for (int i=1;i<=n;i++){
		cin>>ar[i];
	}

	mins.push_back(make_pair(-2e9,n+1));
	maxs.push_back(make_pair(2e9,n+1));

	for (int i=0;i<=30;i++){
		first_present[i]=n+1;
		first_absent[i]=n+1;
	}

	Build(1,1,n);

	for (int i=n;i>=1;--i){

		for (int j=0;j<=30;j++){
			if (ar[i]&(1<<j)){
				UPD(i+1,first_present[j]-1,(1<<j));
				first_present[j]=i;
			}
			if (!(ar[i]&(1<<j))){
				UPD(i+1,first_absent[j]-1,(1<<j));
				first_absent[j]=i;
			}
		}

/*
		for (int j=1;j<=n;j++){
			cout<<t[j]<<" ";
		}
		cout<<endl;
*/
		while (mins.back().first>ar[i]){
			int ps=mins.back().second;
			int ps_next=mins[mins.size()-2].second;
			UPD(ps,ps_next-1,ar[i]-mins.back().first);
			mins.pop_back();
		}
		mins.push_back(make_pair(ar[i],i));

		while (maxs.back().first<ar[i]){
			int ps=maxs.back().second;
			int ps_next=maxs[maxs.size()-2].second;
			UPD(ps,ps_next-1,-ar[i]+maxs.back().first);
			maxs.pop_back();
		}
		maxs.push_back(make_pair(ar[i],i));

		/*for (int j=1;j<=n;j++){
			cout<<t[j]<<" ";
		}
		cout<<endl;
*/
		//cout<<t[1]<<endl;
		int bound_for_this=get_rmost();
		//cout<<i<<" "<<bound_for_this<<endl;

		update(1,1,n,i,bound_for_this,bound_for_this-i+1);
	}

	for (int i=1;i<=n;i++){
		int here=get(1,1,n,i);
		cout<<here<<endl;
	}

//	cin.get(); cin.get();
	return 0;
}