#include <bits/stdc++.h>

using namespace std;
typedef vector<int> vi;
typedef pair<int, int> ii;
typedef long long ll;
typedef pair<long long, long long> l4;
typedef vector<long long> vll;
typedef double db;
typedef vector<double> vdb;
typedef pair<double, double> dd;
typedef set<int> si;
typedef set<long long> sll;
#define fi first
#define se second
#define matrix(a) vector< vector<a> >
#define sz(a) int((a).size()) 
#define lop(i,a,b) for (int i=a; i<=b; i++)
#define rlop(i,a,b) for (int i=b; i>=a; i--)
#define all(s) (s).begin(),(s).end()
#define pb push_back
#define enter cout<<'\n'
#define lb(i,v) int(lower_bound(all(v),i)-v.begin())
#define ub(i,v) int(upper_bound(all(v),i)-v.begin())
class event{
    public:
    int type;
    int val;
    event(int t,int v){
        type=t;
        val=v;
    }
    event(){
        type=0;
        val=0;
    }
};
template <typename T>
void initialize(int start, vi& stree, vector<T>& level, int l, int u) {
	if (sz(stree) - 1 < start)stree.resize(start + 1);
	if (l == u)stree[start] = l;
	else {
		initialize(2 * start, stree, level, l, (u + l) / 2);
		initialize(2 * start + 1, stree, level, (u + l) / 2 + 1, u);
		if (level[stree[start * 2]] < level[stree[start * 2 + 1]])stree[start] = stree[start * 2];
		else stree[start] = stree[start * 2 + 1];
	}
	return;
}
template <typename T> 
int rmq(int start, vi& stree,vector<T>& level,int i, int j, int l, int u) {
	if (i > j)swap(i, j);
	if (j<l || i>u)return -1;
	if (l >= i&&u <= j)return stree[start];
	int t1 = rmq(2 * start, stree, level, i, j, l, (u + l) / 2);
	int t2 = rmq(2 * start + 1, stree, level, i, j, (u + l) / 2 + 1, u);
	if (t1 == -1)return t2;
	if (t2 == -1)return t1;
	if (level[t1] < level[t2])return t1;
	return t2;
}
int main() {
    int n,k;
    cin >> n >> k;
    vector<int> a(n),preand(n),preor(n),na(n);
    for(int i = 0; i < n; i++){
       cin >> a[i];
        na[i]=-a[i];
       if(i){
           preand[i]=a[i]&preand[i-1];
           preor[i]=a[i]|preor[i-1];
       }
        else{
            preand[i]=a[i];
            preor[i]=a[i];
        }
    }
    vi stree,nstree;
    initialize<int>(1,stree,a,0,n-1);
    initialize<int>(1,nstree,na,0,n-1);
    vi interval(n,-1);
    matrix(event) b(n+1);
    int rightmost=-1;
    lop(i,0,n-1){
        int start=max(i,rightmost+1);
        if(start>n-1)break;
        int aand=preand[start],aor=preor[start],mini=a[rmq<int>(1,stree,a,i,start,0,n-1)],maxi=a[rmq<int>(1,nstree,na,i,start,0,n-1)];
        if(i){
            aand^=(!preand[i-1]);
            aor^=preor[i-1];
        }
        if(aor-aand-maxi+mini>=k)interval[i]=start;
        lop(j,start+1,n-1){
            mini=min(mini,a[j]);
            maxi=max(maxi,a[j]);
            aand&=a[j];
            aor|=a[j];
            if(aor-aand-maxi+mini>=k)interval[i]=j;
        }
        rightmost=max(rightmost,interval[i]);
        if(interval[i]!=-1){
            int length=interval[i]-i+1;
            b[i].pb(event(1,length));
            b[interval[i]+1].pb(event(2,length));
        }
    }
    multiset<int> ms;
    ms.insert(-1);
    lop(i,0,n-1){
        lop(j,0,sz(b[i])-1){
            if(b[i][j].type==1)ms.insert(b[i][j].val);
            else{
                multiset<int>::iterator it=ms.find(b[i][j].val);
                ms.erase(it);
            }
        }
        cout<<*(--ms.end())<<'\n';
    }
    return 0;
}