import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;
import java.util.TreeSet;

public class D2 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni(), K = ni();
		int[] a = na(n);
		
		int[] ra = new int[n];
		for(int i = 0;i < n;i++)ra[i] = -a[i];
		
		int[][] stmin = build(a);
		int[][] stmax = build(ra);
		
		int[][] efs = new int[80*n][];
		int efp = 0;
		int esp = 0;
		
		int[][] oas = new int[0][];
		for(int i = n-1;i >= 0;i--){
			int[][] noas = new int[40][];
			int p = 0;
			for(int j = 0;j < oas.length;j++){
				oas[j][0] |= a[i];
				oas[j][1] &= a[i];
				if(p > 0 && noas[p-1][0] == oas[j][0] && 
						noas[p-1][1] == oas[j][1]){
					noas[p-1][2] = oas[j][2];
				}else{
					noas[p++] = oas[j];
				}
			}
			if(!(p > 0 && noas[p-1][0] == a[i] && 
					noas[p-1][1] == a[i])){
				noas[p++] = new int[]{a[i], a[i], i};
			}else{
				noas[p-1][2] = i;
			}
			oas = Arrays.copyOf(noas, p);
			
//			tr(i, oas);
			
			int to = n;
			for(int[] oa : oas){
				// [oa[2], to)
				int cha = oa[0] - oa[1];
				int low = oa[2]-1, high = to;
				while(high - low > 1){
					int h = high+low>>1;
					// [i,h]
//					tr(h, oa, to, cha, -rmq(stmax, i, h+1) - rmq(stmin, i, h+1));
					if(cha - (-rmq(stmax, i, h+1) - rmq(stmin, i, h+1)) >= K){
						low = h;
					}else{
						high = h;
					}
				}
				if(low >= oa[2]){
//					tr(i, oa, to, low);
					efs[efp++] = new int[]{i, low - i + 1, i};
					efs[efp++] = new int[]{low+1, low - i + 1, i};
				}
				to = oa[2];
			}
		}
		
		int I = -1;
		int[] anss = new int[n];
		Arrays.fill(anss, I);
		
		Arrays.sort(efs, 0, efp, new Comparator<int[]>() {
			public int compare(int[] a, int[] b) {
				return a[0] - b[0];
			}
		});
		TreeSet<Long> set = new TreeSet<Long>();
		
		int q = 0;
		for(int i = 0;i < n;i++){
			while(q < efp && efs[q][0] <= i){
				long code = (long)efs[q][1]<<32|efs[q][2];
				if(set.contains(code)){
					set.remove(code);
				}else{
					set.add(code);
				}
				q++;
			}
			if(!set.isEmpty()){
				Long first = set.last();
				anss[i] = Math.max(anss[i], (int)(first>>>32));
			}
		}
		
		for(int v : anss){
			out.println(v);
		}
	}
	
	public static int[][] build(int[] a)
	{
		int n = a.length;
		int b = 32-Integer.numberOfLeadingZeros(n);
		int[][] ret = new int[b][];
		for(int i = 0, l = 1;i < b;i++, l*=2) {
			if(i == 0) {
				ret[i] = a;
			}else {
				ret[i] = new int[n-l+1];
				for(int j = 0;j < n-l+1;j++) {
					ret[i][j] = Math.min(ret[i-1][j], ret[i-1][j+l/2]);
				}
			}
		}
		return ret;
	}
	
	// [a,b)
	public static int rmq(int[][] or, int l, int r)
	{
		assert l <= r;
		if(l >= r)return Integer.MAX_VALUE;
		// 1:0, 2:1, 3:1, 4:2, 5:2, 6:2, 7:2, 8:3
		int t = 31-Integer.numberOfLeadingZeros(r-l);
		return Math.min(or[t][l], or[t][r-(1<<t)]);
	}

	
	void run() throws Exception
	{
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new D2().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
}