Little Bolek has found a picture with n mountain peaks painted on it. The n painted peaks are represented by a non-closed polyline, consisting of 2n segments. The segments go through 2n + 1 points with coordinates (1, y1), (2, y2), ..., (2n + 1, y2n + 1), with the i-th segment connecting the point (i, yi) and the point (i + 1, yi + 1). For any even i (2 ≤ i ≤ 2n) the following condition holds: yi - 1 < yi and yi > yi + 1. 

We shall call a vertex of a polyline with an even x coordinate a mountain peak.

<image> The figure to the left shows the initial picture, the figure to the right shows what the picture looks like after Bolek's actions. The affected peaks are marked red, k = 2. 

Bolek fancied a little mischief. He chose exactly k mountain peaks, rubbed out the segments that went through those peaks and increased each peak's height by one (that is, he increased the y coordinate of the corresponding points). Then he painted the missing segments to get a new picture of mountain peaks. Let us denote the points through which the new polyline passes on Bolek's new picture as (1, r1), (2, r2), ..., (2n + 1, r2n + 1).

Given Bolek's final picture, restore the initial one.

Input

The first line contains two space-separated integers n and k (1 ≤ k ≤ n ≤ 100). The next line contains 2n + 1 space-separated integers r1, r2, ..., r2n + 1 (0 ≤ ri ≤ 100) — the y coordinates of the polyline vertices on Bolek's picture.

It is guaranteed that we can obtain the given picture after performing the described actions on some picture of mountain peaks.

Output

Print 2n + 1 integers y1, y2, ..., y2n + 1 — the y coordinates of the vertices of the polyline on the initial picture. If there are multiple answers, output any one of them.

Examples

Input

3 2
0 5 3 5 1 5 2


Output

0 5 3 4 1 4 2 


Input

1 1
0 2 0


Output

0 1 0 
import java.io.BufferedWriter;
import java.io.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.util.Locale;

public class A218 
{
	public static void main(String[] args) throws IOException 
	{
		setStandardIO();
		//setFileIO("test");		
		
		int n = nextInt() * 2 + 1;
		int k = nextInt();
		int tab[] = new int[n];
		
		for (int i = 0; i < tab.length; i++) {
			tab[i] = nextInt();
		}
		
		for (int i = 0; i < tab.length; i++) {
			if (i % 2 == 1 && tab[i] > tab[i - 1] + 1 && tab[i] > tab[i + 1] + 1 && k > 0) {
				tab[i]--;
				k--;
			}
			print(tab[i] + " ");		
		}

		flush();
	}

	// ~ -----------------------------------------------------------------------
	// ~ - Auxiliary code ------------------------------------------------------
	// ~ -----------------------------------------------------------------------
	static InputStream in;
	static PrintWriter out;

	/**
	 * Simple buffered reader class. Reads if buffer is empty. Try to fill up
	 * whole buffer.
	 */
	public static class SimpleBufferedInputStream extends InputStream 
	{
		// ~ Static fields / Initializers --------------------------------------
		private static int defaultCharBufferSize = 16384;
		private InputStream in;
		byte[] buffer;
		int pos = 0;
		int len = 0;
		
		// ~ Constructors ------------------------------------------------------
		public SimpleBufferedInputStream(InputStream in) {
			this(in, defaultCharBufferSize);
		}

		public SimpleBufferedInputStream(InputStream in, int size) {
			this.in = in;
			this.buffer = new byte[size];
		}
	    
		// ~ Methods -----------------------------------------------------------
		@Override
		public int read() throws IOException {
			if (pos < len)
				return buffer[pos++];
			
			len = in.read(buffer);
			if (len == -1)
				return len;
			
			pos = 0;
			if (len <= 0)
				return -1;
			
			return buffer[pos++];
		}
	}

	public static void setStandardIO() {
		in = new SimpleBufferedInputStream(System.in);
		out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
	}

	public static void setFileIO(String fileName) throws IOException {
		in = new SimpleBufferedInputStream(new FileInputStream(fileName + ".in"));
 		out = new PrintWriter(new BufferedWriter(new FileWriter(fileName + ".out")));
	}

	public static int skipWhitespaces() throws IOException {
		int c;
		for (;;) {
			c = in.read();
			if (c == -1) throw new IOException();
			if (!isWhitespace(c)) break;
		}	
		
		return c;
	}
	
	public static int skipNewLines() throws IOException {
		int c;
		for (;;) {
			c = in.read();
			if (c == -1) throw new IOException();
			if (!isNewLine(c)) break;
		}	
		
		return c;
	}

	public static boolean isNewLine(int c) {
		return c == '\n' || c == '\r' ? true : false;
	}

	public static boolean isWhitespace(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' ? true : false;
	}
	
	public static int nextNoWhitespace() throws IOException {
		int c = in.read();
		if (c == -1 || isWhitespace(c)) return -1;
		
		return c;
	}

	public static int nextNoNewLine() throws IOException {
		int c = in.read();
		if (c == -1 || isNewLine(c)) return -1;
		
		return c;
	}

	public static long nextLong() throws IOException {
		int c;
		for (;;) {
			c = in.read();
			if (!isWhitespace(c)) break;
			if (c == -1) throw new RuntimeException();
		}	

		boolean neg = false;
		long val = 0;
		if (c == '-')
			neg = true;
		else 
			val = c - '0';
		
		for (;;) {
			c = in.read();
			if (isWhitespace(c) || c == -1) 
				break;
			
			val = val * 10 + (c - '0');
		}

		if (neg) 
			return -val;
		
		return val;
	}

	public static int nextInt() throws IOException {
		int c;
		for (;;) {
			c = in.read();
			if (!isWhitespace(c)) break;
			if (c == -1) throw new RuntimeException();
		}	
		
		boolean neg = false;		
		int val = 0;
		if (c == '-')
			neg = true;
		else 
			val = c - '0';
		
		for (;;) {
			c = in.read();
			if (isWhitespace(c) || c == -1) 
				break;
			
			val = val * 10 + (c - '0');
		}

		if (neg) 
			return -val;
		
		return val;
	}

	public static byte nextByte() throws IOException {
		return (byte) nextInt();
	}

	public static String nextLine() throws IOException {
		int c = (char) skipNewLines();
		
		StringBuilder sb = new StringBuilder();
		sb.append((char) c);
		
		for (;;) {
			c = nextNoNewLine();
			if (c == -1)
				break;
			
			sb.append((char) c);
		}

		return sb.toString();
	}

	public static String nextString() throws IOException {
		int c = (char) skipWhitespaces();
		
		StringBuilder sb = new StringBuilder();
		sb.append((char) c);
		
		for (;;) {
			c = nextNoWhitespace();
			if (c == -1)
				break;
			
			sb.append((char) c);
		}

		return sb.toString();
	}

	public static double nextDouble() throws IOException {
		return Double.parseDouble(nextString());
	}	
	
	public static BigDecimal nextBigDecimal() throws IOException {
		return new BigDecimal(nextString());
	}
	
	public static void flush() {
		out.flush();
	}

	public static void println(Object object) {
		out.println(object);
	}

	public static void print(Object object) {
		out.print(object);
	}

	public static void println(double d, int precision) {
		String s = "%1$." + precision + "f";
		out.format(Locale.ENGLISH, s, d);
		out.println();
	}

	public static void println(BigDecimal d, int precision) {
		String s = "%1$." + precision + "f";
		out.format(Locale.ENGLISH, s, d);
		out.println();
	}
}
