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.*;
import java.math.*;
import java.util.*;
 
public class practice {

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
 
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
 
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }
 
    }

	static class Reader{
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
 
        public Reader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public String readLine() throws IOException
        {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }
 
        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            }  while ((c = read()) >= '0' && c <= '9');
 
            if (neg)
                return -ret;
            return ret;
        }
 
        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }
 
        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
 
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
 
            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }
 
            if (neg)
                return -ret;
            return ret;
        }
 
        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
 
        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }
 
        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }
	public static void debug(int[][] arr) {
		int r = arr.length;
		int c = arr[0].length;
		int i,j;
		for(i=0;i<r;++i) {
			for(j=0;j<c;++j)  System.err.print(arr[i][j]+" ");
			System.err.println();
		}
	}
	public static void debug(long[][] arr) {
		int r = arr.length;
		int c = arr[0].length;
		int i,j;
		for(i=0;i<r;++i) {
			for(j=0;j<c;++j)  System.err.print(arr[i][j]+" ");
			System.err.println();
		}
	}
	public static void debug(int ...var) {
		for(int i:var)  System.err.print(i+" ");
		System.err.println();
	}
	public static void debug(String ...var) {
		for(String i:var)  System.err.print(i+" ");
		System.err.println();
	}
	public static void debug(double ...var) {
		for(double i:var)  System.err.print(i+" ");
		System.err.println();
	}
	
	public static void debug(long ...var) {
		for(long i:var)  System.err.print(i+" ");
		System.err.println();
	}

    private static Reader scan = new Reader();
    public static void main(String args[]) throws Exception{
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        StringBuilder sb = new StringBuilder();

        /*
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader scan = new InputReader(inputStream);
        */
        
        /*
        PrintWriter out = new PrintWriter(outputStream);
        */

        //be careful of readLine() length of string;
        //Scanner scan = new Scanner(System.in);
        //scan.useDelimiter("");  // for reading character by character
        //BufferedReader
        //BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        //String name = br.readLine();

        int n = scan.nextInt();
        int k = scan.nextInt();
        int total = n+n+1;

        int[] peaks = new int[total];
        for(int i=0;i<total;++i) {
            peaks[i]=scan.nextInt();
        }

        for(int i=1;i<total && k>0;i+=2) {
            --peaks[i];
            if(peaks[i]>peaks[i-1]&&peaks[i]>peaks[i+1]) {
                --k;
            } else {
                ++peaks[i];
            }
        }

        for(int i=0;i<total;++i) {
            sb.append(peaks[i]+" ");
        }

        out.println(sb);                            

        scan.close();
        out.close();

    }
}
