Problem: Walking along a riverside, Mino silently takes a note of something.

"Time," Mino thinks aloud.

"What?"

"Time and tide wait for no man," explains Mino. "My name, taken from the river, always reminds me of this."

"And what are you recording?"

"You see it, tide. Everything has its own period, and I think I've figured out this one," says Mino with confidence.

Doubtfully, Kanno peeks at Mino's records. 

The records are expressed as a string s of characters '0', '1' and '.', where '0' denotes a low tide, '1' denotes a high tide, and '.' denotes an unknown one (either high or low).

You are to help Mino determine whether it's possible that after replacing each '.' independently with '0' or '1', a given integer p is not a period of the resulting string. In case the answer is yes, please also show such a replacement to Mino.

In this problem, a positive integer p is considered a period of string s, if for all 1 ≤ i ≤ \lvert s \rvert - p, the i-th and (i + p)-th characters of s are the same. Here \lvert s \rvert is the length of s.

Input

The first line contains two space-separated integers n and p (1 ≤ p ≤ n ≤ 2000) — the length of the given string and the supposed period, respectively.

The second line contains a string s of n characters — Mino's records. s only contains characters '0', '1' and '.', and contains at least one '.' character.

Output

Output one line — if it's possible that p is not a period of the resulting string, output any one of such strings; otherwise output "No" (without quotes, you can print letters in any case (upper or lower)).

Examples

Input

10 7
1.0.1.0.1.


Output

1000100010


Input

10 6
1.0.1.1000


Output

1001101000


Input

10 9
1........1


Output

No

Note

In the first example, 7 is not a period of the resulting string because the 1-st and 8-th characters of it are different.

In the second example, 6 is not a period of the resulting string because the 4-th and 10-th characters of it are different.

In the third example, 9 is always a period because the only constraint that the first and last characters are the same is already satisfied.

Note that there are multiple acceptable answers for the first two examples, you can print any of them.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.*;
public class Main1
{
    static class Reader 
    { 
        private InputStream mIs;private byte[] buf = new byte[1024];private int curChar,numChars;public Reader() { this(System.in); }public Reader(InputStream is) { mIs = is;} 
        public int read() {if (numChars == -1) throw new InputMismatchException();if (curChar >= numChars) {curChar = 0;try { numChars = mIs.read(buf);} catch (IOException e) { throw new InputMismatchException();}if (numChars <= 0) return -1; }return buf[curChar++];} 
        public String nextLine(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isEndOfLine(c));return res.toString() ;} 
        public String s(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isSpaceChar(c));return res.toString();} 
        public long l(){int c = read();while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }long res = 0; do{ if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read();}while(!isSpaceChar(c));return res * sgn;} 
        public int i(){int c = read() ;while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }int res = 0;do{if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read() ;}while(!isSpaceChar(c));return res * sgn;} 
        public double d() throws IOException {return Double.parseDouble(s()) ;}
        public boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; } 
        public boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; } 
    }
    
    
    ///////////////////////////////////////////////////////////////////////////////////////////
    //    RRRRRRRRR            AAA             HHH     HHH     IIIIIIIIIIIII   LLL           //
    //    RR    RRR           AAAAA            HHH     HHH      IIIIIIIIIII    LLL           //
    //    RR   RRR           AAAAAAA           HHH     HHH          III        LLL           //
    //    RR  RRR           AAA   AAA          HHHHHHHHHHH          III        LLL           //
    //    RRRRRR           AAA     AAA         HHHHHHHHHHH          III        LLL           //
    //    RR  RRR         AAAAAAAAAAAAA        HHH     HHH          III        LLL           //
    //    RR    RRR      AAA         AAA       HHH     HHH      IIIIIIIIIII    LLLLLLLLLLLL  //
    //    RR     RRR    AAA           AAA      HHH     HHH     IIIIIIIIIIIII   LLLLLLLLLLLL  //
    ///////////////////////////////////////////////////////////////////////////////////////////
    
    public static void main(String[] args)throws IOException
    {
        PrintWriter out= new PrintWriter(System.out);
        Reader sc=new Reader();
        int n=sc.i();
        int p=sc.i();
        String s=sc.s();
        char arr[]=s.toCharArray();
        int got=-1;
        for(int i=0;i<n-p;i++)
        {
            if(arr[i]=='1'&&arr[i+p]=='0'||arr[i]=='0'&&arr[i+p]=='1')
            {
                for(int j=0;j<n;j++)
                {
                    if(arr[j]=='.')
                    out.print(1);
                    else
                    out.print(arr[j]);
                }
                out.flush();
                System.exit(0);
            }
            else if(arr[i]=='.'&&arr[i+p]=='1')
            {
                arr[i]='0';
                for(int j=0;j<n;j++)
                {
                    if(arr[j]=='.')
                    out.print(1);
                    else
                    out.print(arr[j]);
                }
                out.flush();
                System.exit(0);
            }
            else if(arr[i]=='.'&&arr[i+p]=='0')
            {
                arr[i]='1';
                for(int j=0;j<n;j++)
                {
                    if(arr[j]=='.')
                    out.print(1);
                    else
                    out.print(arr[j]);
                }
                out.flush();
                System.exit(0);
            }
            else if(arr[i]=='0'&&arr[i+p]=='.')
            {
                arr[i+p]='1';
                for(int j=0;j<n;j++)
                {
                    if(arr[j]=='.')
                    out.print(1);
                    else
                    out.print(arr[j]);
                }
                out.flush();
                System.exit(0);
            }
            else if(arr[i]=='1'&&arr[i+p]=='.')
            {
                arr[i+p]='0';
                for(int j=0;j<n;j++)
                {
                    if(arr[j]=='.')
                    out.print(1);
                    else
                    out.print(arr[j]);
                }
                out.flush();
                System.exit(0);
            }
            else if(arr[i]=='.'&&arr[i+p]=='.')
            {
                arr[i]='0';
                arr[i+p]='1';
                for(int j=0;j<n;j++)
                {
                    if(arr[j]=='.')
                    out.print(1);
                    else
                    out.print(arr[j]);
                }
                out.flush();
                System.exit(0);
            }
        }
        System.out.println("No");
    }
}