Consider the following process. You have a binary string (a string where each character is either 0 or 1) w of length n and an integer x. You build a new binary string s consisting of n characters. The i-th character of s is chosen as follows:

  * if the character w_{i-x} exists and is equal to 1, then s_i is 1 (formally, if i > x and w_{i-x} =  1, then s_i =  1); 
  * if the character w_{i+x} exists and is equal to 1, then s_i is 1 (formally, if i + x ≤ n and w_{i+x} =  1, then s_i =  1); 
  * if both of the aforementioned conditions are false, then s_i is 0. 



You are given the integer x and the resulting string s. Reconstruct the original string w.

Input

The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.

Each test case consists of two lines. The first line contains the resulting string s (2 ≤ |s| ≤ 10^5, each character of s is either 0 or 1). The second line contains one integer x (1 ≤ x ≤ |s| - 1).

The total length of all strings s in the input does not exceed 10^5.

Output

For each test case, print the answer on a separate line as follows:

  * if no string w can produce the string s at the end of the process, print -1; 
  * otherwise, print the binary string w consisting of |s| characters. If there are multiple answers, print any of them. 

Example

Input


3
101110
2
01
1
110
1


Output


111011
10
-1
import java.io.*;
import java.util.*;
public class check3  {

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

        Reader sc=new Reader();
        PrintWriter out = new PrintWriter(System.out);

        int t=sc.nextInt();
        while(t-->0)
        {
            String s=sc.next();
            int x=sc.nextInt();
            int n=s.length();

            int a1[]=new int[n];
            int a2[]=new int[n];
            Arrays.fill(a2,-1);
            for(int i=0;i<n;i++)
            {
                a1[i]=(s.charAt(i)-'0');
            }
            for(int i=0;i<n;i++)
            {
                if(a1[i]==1)
                {
                    if(i-x>=0 && a2[i-x]==-1) a2[i-x]=1;
                    if(i+x<n && a2[i+x]==-1) a2[i+x]=1;
                }
                else if(a1[i]==0)
                {
                    if(i-x>=0) a2[i-x]=0;
                    if(i+x<n) a2[i+x]=0;
                }

            }

            int a3[]=new int[n];
            Arrays.fill(a3,-1);

            for(int i=0;i<n;i++)
            {
                if(a2[i]==-1) a2[i]=0;

                if((i-x)<0 && (i+x)>=n) a3[i]=0;

                else if((i-x)<0) a3[i]=a2[i+x];

                else if((i+x)>=n) a3[i]=a2[i-x];


               else if(a2[i+x]==0 && a2[i-x]==0) a3[i]=0;
               else a3[i]=1;
            }
            boolean flag=true;
            for(int i=0;i<n;i++)
            {
                if(a1[i]!=a3[i])
                {
                    flag=false;
                    break;
                }
            }
            //System.out.println(s+" "+Arrays.toString(a1)+Arrays.toString(a2)+Arrays.toString(a3));
            if(flag==false) System.out.println(-1);
            else
            {
                for(int i=0;i<n;i++)
                    System.out.print(a2[i]);
                System.out.println();
            }




        }
        out.flush();
    }


    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 nextLine() 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 boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() throws IOException{
            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 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();
        }

    }

}