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.util.*;



public class ModifyLongest {

    InputStream is;

    PrintWriter out;

    String INPUT = "";

    //boolean codechef=true;

    boolean codechef=true;



    void solve()

    {
        int n=ni(),p=ni();
        char[] arr=ns(n);
        if(p>n)
        {
            System.out.println("No");
            return;
        }
        int r=(n/p)+1,c=p;
        char[][] ch=new char[r][c];
        int ind=0;
        for(int i=0;i<r;i++)
        {
            for(int j=0;j<c;j++)
            {
                if(ind<n)
                {
                    ch[i][j]=arr[ind++];
                }
                else
                {
                    ch[i][j]='.';
                }
                //System.out.print(ch[i][j]+" ");
            }
            //System.out.println();
        }

        for(int i=0;i<c;i++)
        {
            int[] cnt=new int[2];
            for(int j=0;j<r;j++)
            {
                if(ch[j][i]=='.')
                {
                    if(j==0)
                    {
                        if(ch[j+1][i]!='0')ch[j][i]='0';
                        else ch[j][i]='1';
                    }
                    else
                    {
                        if(ch[j-1][i]!='0')ch[j][i]='0';
                        else ch[j][i]='1';
                    }
                }
            }
        }
        ind=0;
        for(int i=0;i<r;i++)
        {
            for(int j=0;j<c;j++)
            {
                if(ind<n) {
                    arr[ind++] = ch[i][j];
                }
            }
        }
        for(int j=0;j<n;j++)
        {
            if(arr[j%p]!=arr[j])
            {
                System.out.println(new String(arr));
                return;
            }
        }
        System.out.println("No");
        return;

    }

    static int[] waysToComp(ArrayList<Integer> list,int sz)
    {
        list.sort(new Comparator<Integer>(){

            @Override
            public int compare(Integer o1, Integer o2) {
                return o1.compareTo(o2);
            }
        });
        int lInd=0;
        for(int i=1;i<sz;i++)
        {
            if(list.get(i)>list.get(i-1)+1)
            {
                reverse(list,lInd,i-1);
                lInd=i;
            }
        }
        reverse(list,lInd,sz-1);
        int[] ans=new int[sz];
        for(int i=0;i<sz;i++)
        {
            ans[i]=list.get(i)+i;
        }
        return ans;
    }

    static void reverse(ArrayList<Integer> list,int st,int end)
    {
        //System.out.println(st+" "+end);
        for(int i=st,j=end;i<=j;i++,j--)
        {
            int temp=list.get(i);
            list.set(i,list.get(j));
            list.set(j,temp);
        }
    }


    static int comp(int[][] arr)

    {

        int n=arr.length;

        int m=arr[0].length;

        if(n==1 && m==1)return 1;

        HashSet<Long> vis=new HashSet<>();

        int max=0;

        for(int i=0;i<n;i++)

        {

            for(int j=0;j<m;j++)

            {

                long val;

                if(i>0)

                {

                    val=fnc(arr[i][j],arr[i-1][j]);

                    if(!globalSet.containsKey(val))

                    {

                        max=Math.max(max,comp2(arr,i,j,arr[i][j],arr[i-1][j]));

                        vis.add(val);

                    }

                    else if(!globalSet.get(val).contains(fnc2(i,j)))

                    {

                        max=Math.max(max,comp2(arr,i,j,arr[i][j],arr[i-1][j]));

                        vis.add(val);

                    }

                }



                if(i<n-1)

                {

                    val=fnc(arr[i][j],arr[i+1][j]);

                    if(!globalSet.containsKey(val))

                    {

                        max=Math.max(max,comp2(arr,i,j,arr[i][j],arr[i+1][j]));

                        vis.add(val);

                    }

                    else if(!globalSet.get(val).contains(fnc2(i,j)))
                    {

                        max=Math.max(max,comp2(arr,i,j,arr[i][j],arr[i+1][j]));

                        vis.add(val);

                    }

                }





                if(j>0)

                {

                    val=fnc(arr[i][j],arr[i][j-1]);



                    if(!globalSet.containsKey(val))

                    {

                        max=Math.max(max,comp2(arr,i,j,arr[i][j],arr[i][j-1]));

                        vis.add(val);

                    }

                    else if(!globalSet.get(val).contains(fnc2(i,j)))

                    {

                        max=Math.max(max,comp2(arr,i,j,arr[i][j],arr[i][j-1]));

                        vis.add(val);

                    }

                }





                if(j<m-1)

                {

                    val=fnc(arr[i][j],arr[i][j+1]);



                    if(!globalSet.containsKey(val))

                    {

                        max=Math.max(max,comp2(arr,i,j,arr[i][j],arr[i][j+1]));

                        vis.add(val);

                    }

                    else if(!globalSet.get(val).contains(fnc2(i,j)))

                    {

                        max=Math.max(max,comp2(arr,i,j,arr[i][j],arr[i][j+1]));

                        vis.add(val);

                    }

                }



            }

        }


        return max;

    }



    static HashMap<Long,HashSet<Long>> globalSet;



    static int comp2(int[][] arr,int i,int j,int a,int b)

    {

        //System.out.println(a+" "+b);

        int n=arr.length,m=arr[0].length;

        Queue<Pair> queue=new LinkedList<>();

        HashSet<Long> vis=new HashSet<Long>();



        Pair pr=new Pair(i,j);

        queue.add(pr);

        vis.add(fnc2(i,j));

        int cnt=0;

        while(!queue.isEmpty())

        {

            Pair curr=queue.poll();

            int curri=curr.a,currj=curr.b;



            //System.out.println(curri+":"+currj);

            cnt++;

            if(curri>0)

            {

                if(arr[curri-1][currj]==a || arr[curri-1][currj]==b)

                {

                    Pair tmp=new Pair(curri-1,currj);

                    long val=fnc2(curri-1,currj);

                    if(!vis.contains(val))

                    {

                        queue.add(tmp);

                        vis.add(val);

                    }

                }

            }



            if(currj>0)

            {

                if(arr[curri][currj-1]==a || arr[curri][currj-1]==b)

                {

                    Pair tmp=new Pair(curri,currj-1);

                    long val=fnc2(curri,currj-1);

                    if(!vis.contains(val))

                    {

                        queue.add(tmp);

                        vis.add(val);

                    }

                }

            }



            if(curri<n-1)

            {

                if(arr[curri+1][currj]==a || arr[curri+1][currj]==b)

                {

                    Pair tmp=new Pair(curri+1,currj);

                    long val=fnc2(curri+1,currj);

                    if(!vis.contains(val))

                    {

                        queue.add(tmp);

                        vis.add(val);

                    }

                }

            }



            if(currj<m-1)

            {

                if(arr[curri][currj+1]==a || arr[curri][currj+1]==b)

                {

                    Pair tmp=new Pair(curri,currj+1);

                    long val=fnc2(curri,currj+1);

                    if(!vis.contains(val))

                    {

                        queue.add(tmp);

                        vis.add(val);

                    }

                }

            }

        }

        if(globalSet.containsKey(fnc(a,b)))
        {
            HashSet<Long> inset=globalSet.get(fnc(a,b));
            inset.addAll(vis);
        }
        else
        {
            globalSet.put(fnc(a,b),vis);
        }


        //System.out.println(cnt);

        return cnt;

    }





    static long fnc(int a,int b)

    {

        long val=Math.min(a,b)*1000000007;

        val+=Math.max(a,b);

        return val;

    }



    static long fnc2(int a,int b)

    {

        long val=a*1000000007;

        val+=b;

        return val;

    }





    static class Pair

    {

        int a,b;

        public Pair(int a,int b)

        {

            this.a=a;

            this.b=b;

        }

    }



    static int bit[];



    static void add(int x,int d,int n)

    {

        for(int i=x;i<=n;i+=i&-i)bit[i]+=d;

    }



    static int query(int x)

    {

        int ret=0;

        for(int i=x;i>0;i-=i&-i)

            ret+=bit[i];

        return ret;

    }



    static long lcm(int a,int b)

    {

        long val=a;

        val*=b;

        return (val/gcd(a,b));

    }



    static int gcd(int a,int b)

    {

        if(a==0)return b;

        return gcd(b%a,a);

    }



    static int pow(int a, int b, int p)

    {

        long ans = 1, base = a;

        while (b!=0)

        {

            if ((b & 1)!=0)

            {

                ans *= base;

                ans%= p;

            }

            base *= base;

            base%= p;

            b >>= 1;

        }

        return (int)ans;

    }



    static int inv(int x, int p)

    {

        return pow(x, p - 2, p);

    }





    void run() throws Exception

    {

        if(codechef)oj=true;

        is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());

        out = new PrintWriter(System.out);



        long s = System.currentTimeMillis();

        solve();

        out.flush();

        tr(System.currentTimeMillis()-s+"ms");

    }



    public static void main(String[] args) throws Exception {new ModifyLongest().run();}



    private byte[] inbuf = new byte[1024];

    public int lenbuf = 0, ptrbuf = 0;



    private int readByte()

    {

        if(lenbuf == -1)throw new InputMismatchException();

        if(ptrbuf >= lenbuf){

            ptrbuf = 0;

            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }

            if(lenbuf <= 0)return -1;

        }

        return inbuf[ptrbuf++];

    }



    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }

    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }



    private double nd() { return Double.parseDouble(ns()); }

    private char nc() { return (char)skip(); }



    private String ns()

    {

        int b = skip();

        StringBuilder sb = new StringBuilder();

        while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')

            sb.appendCodePoint(b);

            b = readByte();

        }

        return sb.toString();

    }



    private char[] ns(int n)

    {

        char[] buf = new char[n];

        int b = skip(), p = 0;

        while(p < n && !(isSpaceChar(b))){

            buf[p++] = (char)b;

            b = readByte();

        }

        return n == p ? buf : Arrays.copyOf(buf, p);

    }



    private char[][] nm(int n, int m)

    {

        char[][] map = new char[n][];

        for(int i = 0;i < n;i++)map[i] = ns(m);

        return map;

    }



    private int[] na(int n)

    {

        int[] a = new int[n];

        for(int i = 0;i < n;i++)a[i] = ni();

        return a;

    }



    private int ni()

    {

        int num = 0, b;

        boolean minus = false;

        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));

        if(b == '-'){

            minus = true;

            b = readByte();

        }



        while(true){

            if(b >= '0' && b <= '9'){

                num = num * 10 + (b - '0');

            }else{

                return minus ? -num : num;

            }

            b = readByte();

        }

    }



    private long nl()

    {

        long num = 0;

        int b;

        boolean minus = false;

        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));

        if(b == '-'){

            minus = true;

            b = readByte();

        }



        while(true){

            if(b >= '0' && b <= '9'){

                num = num * 10 + (b - '0');

            }else{

                return minus ? -num : num;

            }

            b = readByte();

        }

    }



    private boolean oj = System.getProperty("ONLINE_JUDGE") != null;

    private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }

}