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.*;

/**
 * Works good for CF
 * @author cykeltillsalu
 */
public class A134_div2 {

    //some local config
    static boolean test = false;
    static String testDataFile = "testdata.txt";
    static String feedFile = "feed.txt";
    CompetitionType type = CompetitionType.CF;
    private static String ENDL = "\n";

    // solution
    private void solve() throws Throwable {
        int n = iread(), k = iread();
        n = n*2 +1;
        int[] height = new int[n];

        for(int i = 0; i < n; i++){
            height[i] = iread();
        }

        for(int i = 1; i < n; i += 2){
            if(k ==0){
                break;
            }
            if(height[i]-1 > height[i-1] && height[i]-1 > height[i+1]){
                height[i] --;
                k --;
            }
        }
        for(int i = 0; i < n; i ++){
            out.write(height[i] + "");
            if(i < n-1){
                out.write(" ");
            }
        }
        out.write("\n");
        out.flush();
    }

    public int iread() throws Exception {
        return Integer.parseInt(wread());
    }

    public double dread() throws Exception {
        return Double.parseDouble(wread());
    }

    public long lread() throws Exception {
        return Long.parseLong(wread());
    }

    public String wread() throws IOException {
        StringBuilder b = new StringBuilder();
        int c;
        c = in.read();
        while (c >= 0 && c <= ' ')
            c = in.read();
        if (c < 0)
            return "";
        while (c > ' ') {
            b.append((char) c);
            c = in.read();
        }
        return b.toString();
    }

    public static void main(String[] args) throws Throwable {

        if(test){ //run all cases from testfile:
            BufferedReader testdataReader = new BufferedReader(new FileReader(testDataFile));
            String readLine = testdataReader.readLine();
            int casenr = 0;
            out: while (true) {
                BufferedWriter w = new BufferedWriter(new FileWriter(feedFile));
                if(!readLine.equals("input")){
                    break;
                }
                while (true) {
                    readLine = testdataReader.readLine();
                    if(readLine.equals("output")){
                        break;
                    }
                    w.write(readLine + "\n");
                }
                w.close();
                System.out.println("Answer on case "+(++casenr)+": ");

                new A134_div2().solve();
                System.out.println("Expected answer: ");


                while (true) {
                    readLine = testdataReader.readLine();

                    if(readLine == null){
                        break out;
                    }
                    if(readLine.equals("input")){
                        break;
                    }
                    System.out.println(readLine);
                }
                System.out.println("----------------");
            }
            testdataReader.close();
        } else { // run on server
            new A134_div2().solve();
        }
        out.close();
    }

    public A134_div2() throws Throwable {
        if (test) {
            in = new BufferedReader(new FileReader(new File(feedFile)));
        }
    }

    InputStreamReader inp = new InputStreamReader(System.in);
    BufferedReader in = new BufferedReader(inp);
    static BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));

    enum CompetitionType {CF, OTHER};
}