#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef pair<ll,ll> pll;
typedef vector<bool> vb;
const ll oo = 0x3f3f3f3f3f3f3f3f;
const double eps = 1e-9;
#define sz(c) ll((c).size())
#define all(c) begin(c), end(c)
#define FOR(i,a,b) for (ll i = (a); i < (b); i++)
#define FORD(i,a,b) for (ll i = (b)-1; i >= (a); i--)
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define eb emplace_back
#define xx first
#define yy second
#define has(c,i) ((c).find(i) != end(c))
#define DBGDO(X) ({ if(1) cerr << "DBGDO: " << (#X) << " = " << (X) << endl; })

typedef function<ll(ll,ll)> binop;

struct bit {
	ll n;
	ll ZERO;
	binop op;
	vl a;

	bit(ll n, ll ZERO, binop op): n(n), ZERO(ZERO), op(op), a(n+2,ZERO) { }

	void add(ll i, ll v) {
		for (++i; i <= n+1; i += i & -i) a[i] = op(a[i],v);
	}

	ll get(ll i) {
		ll res = ZERO;
		for (++i; i; i -= i & -i) res = op(res,a[i]);
		return res;
	}
};

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	
	ll n, k; cin >> n >> k;
	vl a(n);
	FOR(i,0,n) cin >> a[i];
	
	bit b_or (n,   0, bit_or <ll>());
	bit b_and(n,  ~0, bit_and<ll>());
	bit b_max(n, -oo, [&](const ll &x, const ll &y) { return max(x,y); });
	bit b_min(n,  oo, [&](const ll &x, const ll &y) { return min(x,y); });
	
	vector<pll> os, as;

	auto normalize = [&](vector<pll> &vs) {
		vector<pll> nvs;
		FOR(i,0,sz(vs)) {
			if (i+1 < sz(vs) && vs[i].yy == vs[i+1].yy) continue;
			nvs.pb(vs[i]);
		}
		vs = nvs;
	};
	
	vl ress(n,-1);
	FORD(i,0,n) {
		b_max.add(i,a[i]);
		b_min.add(i,a[i]);
		
		os.eb(i,a[i]);
		for (auto &p: os) p.yy |= a[i];
		normalize(os);
		
		as.eb(i,a[i]);
		for (auto &p: as) p.yy &= a[i];
		normalize(as);
		
		
		vector<pll> ev = {{n,0}};
		for (auto p: os) ev.pb(p);
		for (auto p: as) ev.pb(p);
		sort(all(ev));
		
		ll cur = i-1;

		ll co = a[i], ca = a[i];
		
		auto score = [&](ll j) {
			return (co - ca) - (b_max.get(j) - b_min.get(j));
		};
		
		FOR(j,0,sz(ev)-1) {
			co |= ev[j].yy;
			ca &= ev[j].yy;
			
			ll l = ev[j].xx, r = ev[j+1].xx;
			if (l == r) continue;
			if (score(l) < k) continue;
			while (r-l > 1) {
				ll m = (l+r)/2;
				if (score(m) >= k) l = m; else r = m;
			}
			cur = max(cur,l);			
		}
		if (cur >= i) ress[i] = cur;
	}
	
	vl res(n,-1);

	vector<tuple<ll,ll,bool>> ev;
	FOR(i,0,n) if (ress[i] != -1) {
		ll len = ress[i]-i+1;
		ev.eb(i,len,true);
		ev.eb(ress[i]+1,len,false);
	}
	sort(all(ev));
	
	map<ll,ll> cnt;
	ll j = 0;
	FOR(i,0,n) {
		while (j < sz(ev) && get<0>(ev[j]) == i) {
			ll len = get<1>(ev[j]);
			if (get<2>(ev[j])) cnt[len]++; else cnt[len]--;
			if (cnt[len] == 0) cnt.erase(len);
			j++;
		}
		if (sz(cnt)) res[i] = max(res[i],cnt.rbegin()->xx);
	}

	FOR(i,0,n) cout << res[i] << "\n";
}