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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

import static java.lang.Math.log;
import static java.lang.Math.min;

public class First {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        int t;
        t = in.nextInt();
        //t = 1;
        while (t > 0) {
            solver.call(in,out);
            t--;
        }
        out.close();

    }

    static class TaskA {
        public void call(InputReader in, PrintWriter out) {
            String s;
            s = in.next();

            int n ,a ,b;
            n = s.length();
            a = in.nextInt();

            int[] arr = new int[n];
            int[] array = new int[n];

            for (int i = 0; i < n; i++) {
                arr[i] = Integer.parseInt(String.valueOf(s.charAt(i)));
            }

            Arrays.fill(array, 1);

            for (int i = 0; i < n; i++) {
                if(arr[i]==0) {
                    if (a + i < n) {
                        array[a+i] = 0;
                    }
                    if(i-a>=0){
                        array[i-a] = 0;
                    }
                }
            }

            for (int i = 0; i < n; i++) {
                if(arr[i]==1){
                    b =0;
                    if(i-a>=0){
                        if(array[i-a]==1){
                            b++;
                        }
                    }
                    if(i+a<n){
                        if(array[i+a]==1){
                            b++;
                        }
                    }
                    if(b==0){
                        out.println("-1");
                        return;
                    }

                }
            }

            for (int i = 0; i < n; i++) {
                out.print(array[i]);
            }
            out.println();







        }
    }

    static class answer implements Comparable<answer> {
        int a, b;

        public answer(int a, int b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public int compareTo(answer o) {
            return o.a - this.a;
        }
    }

    static class arrayList {
        ArrayList<Integer> arrayList = new ArrayList<>();
    }

    static long gcd(long a, long b)
    {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    static void sort(int[] a) {
        ArrayList<Integer> l=new ArrayList<>();
        for (int i:a) l.add(i);
        Collections.sort(l);
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }

    static final Random random=new Random();

    static void shuffleSort(int[] arr) {
        int n=arr.length;
        for (int i=0; i<n; i++) {
            int a=random.nextInt(n), temp=arr[a];
            arr[a]=arr[i];
            arr[i]=temp;
        }
        Arrays.sort(arr);
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong(){
            return Long.parseLong(next());
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }

    }
}