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.io.*;
    import java.lang.reflect.Array;
    import java.math.BigInteger;
    import java.util.*;
     
    public class Main {
     
    	private static InputStream stream;
    	private static byte[] buf = new byte[1024];
    	private static int curChar;
    	private static int numChars;
    	private static SpaceCharFilter filter;
    	private static PrintWriter pw;
    	public static final long mod = (long)1e9+7;
        public static void main(String[] args) {
        	InputReader(System.in);
    		pw = new PrintWriter(System.out); 
            new Thread(null ,new Runnable(){
               public void run(){
                   try{
                       test();//This is solution method
               pw.close();
           } catch(Exception e){
               e.printStackTrace();
           }
       }
    },"1",1<<26).start();
            }
        public static void test() throws IOException{
       
       	int t=1;
       	while(t-->0){
       	
       		solve();
       		//pw.println();
       		//sb.append("\n");	
       	}
       	//pw.println(sb);
       }
        static int st[];
        private static void solve(){

        	HashSet<Integer> prime = new HashSet<Integer>();
        	for(int i=2;i<=1;i++) {
        		if(isPrime(i)) {
        			prime.add(i);
        		}
        	}

        	int n=nextInt();
        	int p=nextInt();
        	String s=nextLine();
        	int array[] = new int[s.length()+1];
        	for(int i=1;i<=s.length();i++) {
        		if(s.charAt(i-1)=='.')
        			array[i] = -1;
        		else
        			array[i] = s.charAt(i-1)-'0';
        	}
        	
        	for(int i=1;i<=s.length()-p;i++) {
        		if(array[i] == -1) {
        			if(array[i+p]==-1) {
        				array[i] = 0;
        				array[i+p] = 1;
        			}else {
        				array[i] = 1^array[i+p];
        			}
        		}else {
        			if(array[i+p] == -1) {
        				array[i+p] = 1^array[i];
        			}
        		}
        	}
        for(int i=1;i<=s.length();i++)	
        	if(array[i]==-1)
        		array[i]=0;
        for(int i=1;i<=s.length()-p;i++) {
        	if(array[i]!=array[i+p]) {
        		for(int j=1;j<=s.length();j++) {
        			pw.print(array[j]);
        		}
        		return;
        	}
        }
        pw.println("No");
     }
        private static boolean isPalindrome(int freq[]){
    		int odd=0;
    		for(int i=0;i<26;i++){
    			if(freq[i]%2!=0){
    				odd++;
    			}
    		}
    		if(odd==1)
    			return true;
    		return false;
    	}
    		
        public static boolean isPrime(long n) {
    		if (n <= 1)
    			return false;
    		if (n <= 3)
    			return true;
     
    		if (n % 2 == 0 || n % 3 == 0)
    			return false;
     
    		for (long i = 5; i * i <= n; i = i + 6)
    			if (n % i == 0 || n % (i + 2) == 0)
    				return false;
     
    		return true;
    	}
        public static boolean check(int x,int y,int n){
        	if(x>=0 && x<n && y>=0 && y<n)
        		return true;
        	return false;
        }
       
    private static void update(int node,int low,int high,int ind,int val){
        	 if(ind < low || ind > high){
                 return;
             }
    		
    		if(low==high){
         		st[node]=val;
         		return;
        	 }
        	 
        	int mid=(low+high)/2;
        	if(low<= ind && ind<=mid){
        		update(2*node, low, mid, ind, val);
        	}else{
        		update(2*node+1, mid+1, high, ind, val);
        	}
         st[node]= st[2*node] + st[2*node+1];
    }
        
    private static int query(int node,int low,int high,int qlow,int qhigh){
        	
        	if(qlow>high || qhigh<low){
        		return 0;
        	}
        	 
        	if(qlow<=low && qhigh>=high){
            	
        		return st[node];
        	}
        	
        int mid=(low+high)/2;
        int ans1=query(2*node, low, mid, qlow, qhigh);
        int ans2=query(2*node+1, mid+1, high, qlow, qhigh);
        
        return ans1 + ans2;
        }
        
        
     
     // To Get Input
     // Some Buffer Methods
      
         		     	
         		    	public static void InputReader(InputStream stream1) {
         		    		stream = stream1;
         		    	}
      
         		    	private static boolean isWhitespace(int c) {
         		    		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
         		    	}
      
         		    	private static boolean isEndOfLine(int c) {
         		    		return c == '\n' || c == '\r' || c == -1;
         		    	}
      
         		    	private static int read() {
         		    		if (numChars == -1)
         		    			throw new InputMismatchException();
         		    		if (curChar >= numChars) {
         		    			curChar = 0;
         		    			try {
         		    				numChars = stream.read(buf);
         		    			} catch (IOException e) {
         		    				throw new InputMismatchException();
         		    			}
         		    			if (numChars <= 0)
         		    				return -1;
         		    		}
         		    		return buf[curChar++];
         		    	}
      
         		    	private static int nextInt() {
         		    		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;
         		    	}
      
         		    	private static long nextLong() {
         		    		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;
         		    	}
      
         		    	private static String nextToken() {
         		    		int c = read();
         		    		while (isSpaceChar(c))
         		    			c = read();
         		    		StringBuilder res = new StringBuilder();
         		    		do {
         		    			res.appendCodePoint(c);
         		    			c = read();
         		    		} while (!isSpaceChar(c));
         		    		return res.toString();
         		    	}
      
         		    	private static 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();
         		    	}
      
         		    	private static int[] nextIntArray(int n) {
         		    		int[] arr = new int[n];
         		    		for (int i = 0; i < n; i++) {
         		    			arr[i] = nextInt();
         		    		}
         		    		return arr;
         		    	}
      
         		    	private static long[][] next2dArray(int n, int m) {
         		    		long[][] arr = new long[n][m];
         		    		for (int i = 0; i < n; i++) {
         		    			for (int j = 0; j < m; j++) {
         		    				arr[i][j] = nextLong();
         		    			}
         		    		}
         		    		return arr;
         		    	}
         		    	private static char[][] nextCharArray(int n,int m){
         		    		char [][]c=new char[n][m];
         		    		for(int i=0;i<n;i++){
         		    			String s=nextLine();
         		    			for(int j=0;j<s.length();j++){
         		    				c[i][j]=s.charAt(j);
         		    			}
         		    		}
         		    		return c;
         		    	}
      
         		    	private static long[] nextLongArray(int n) {
         		    		long[] arr = new long[n];
         		    		for (int i = 0; i < n; i++) {
         		    			arr[i] = nextLong();
         		    		}
         		    		return arr;
         		    	}
      
         		    	private static void pArray(int[] arr) {
         		    		for (int i = 0; i < arr.length; i++) {
         		    			pw.print(arr[i] + " ");
         		    		}
         		    		pw.println();
         		    		return;
         		    	}
      
         		    	private static void pArray(long[] arr) {
         		    		for (int i = 0; i < arr.length; i++) {
         		    			pw.print(arr[i] + " ");
         		    		}
         		    		pw.println();
         		    		return;
         		    	}
      
         		    	private static void pArray(boolean[] arr) {
         		    		for (int i = 0; i < arr.length; i++) {
         		    			pw.print(arr[i] + " ");
         		    		}
         		    		pw.println();
         		    		return;
         		    	}
      
         		    	private static boolean isSpaceChar(int c) {
         		    		if (filter != null)
         		    			return filter.isSpaceChar(c);
         		    		return isWhitespace(c);
         		    	}
      
         		    	private interface SpaceCharFilter {
         		    		public boolean isSpaceChar(int ch);
         		    	}
        
    }
     
    /*class Pair implements Comparable<Pair>{
    long lit,pri;
     
    public Pair(long x,long y) {
     
    	this.lit=x;
    	this.pri=y;
    }
     
    @Override
    public int compareTo(Pair arg0) {
    	if((double)lit/(double)pri > (double)arg0.lit/(double)arg0.pri){
    		return 1;
    	}
    	if((double)lit/(double)pri < (double)arg0.lit/(double)arg0.pri){
    		return -1;
    	}
    	return 0;
    //	return 0;
    }
    }
    */