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
//package com.company;
//  IMPORT PACKAGE//-------------->>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
import java.util.*;
import java.util.function.Function;
import java.util.stream.Collectors;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Random;
import java.util.StringTokenizer;
import java.io.*;
import java.math.*;


public class Main {

//INPUT READER//

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public 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++];
        }

        public int Int() {
            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 String String() {
            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 boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return String();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0)
                    writer.print(' ');
                writer.print(objects[i]);
            }
        }

        public void printLine(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

        public void flush() {
            writer.flush();
        }
    }

    static InputReader in = new InputReader(System.in);
    static OutputWriter out = new OutputWriter(System.out);
    static int modulus = (int) 1e7;

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

    public static long pow(long x, long y) {
        long res = 1;
        while (y > 0) {
            if (y % 2 != 0) {
                res = (res * x) % modulus;
                y--;

            }
            x = (x * x) % modulus;
            y = y / 2;
        }
        return res;
    }

    public static long gcd(long x, long y) {
        if (x == 0)
            return y;
        else
            return gcd(y % x, x);
    }

    public static long lcm(long x, long y) {
        return (x * (y / gcd(x, y)));
    }

    public static int i() {
        return in.Int();
    }

    public static long l() {
        String s = in.String();
        return Long.parseLong(s);
    }

    public static String s() {
        return in.String();
    }

    public static int[] readArray(int n) {
        int A[] = new int[n];
        for (int i = 0; i < n; i++) {
            A[i] = i();
        }
        return A;
    }

    public static long[] readArray(long n) {
        long A[] = new long[(int) n];
        for (int i = 0; i < n; i++) {
            A[i] = l();
        }
        return A;
    }

    static class pair {
        int x;
        int y;

        pair(int x, int y) {
            this.x = x;
            this.y = y;
        }
    }

    static ArrayList<ArrayList<Integer>> graph;
    //static ArrayList<Integer> ans = new ArrayList<>();
    static int po[][];


    public static void dfs(int source, int dest) {
        po[source][dest] = 1;
        ArrayList<Integer> l = graph.get(dest);
        for (int i = 0; i < l.size(); i++) {
            if (po[source][l.get(i)] == 0) {
                dfs(source, l.get(i));

            }
        }

    }
static boolean islegal(int x,int n)
{
    return x>=0 && x<n;
}
{

}
    public static void main(String[] args)
    {
        StringBuffer sb=new StringBuffer();
        int t = i();
        while (t-- > 0)
        {

            String s=s();
            int x=i();
            int n=s.length();
            char c[]=s.toCharArray();
            //ArrayList<Character>ans=new ArrayList<>(n);
            char ans[]=new char[n];
            Arrays.fill(ans,'1');
            int flag=0;
            for(int i=0;i<n;i++)
            {
                if(c[i]=='0')
                {
                    if(islegal(i-x,n))ans[i-x]='0';
                    if(islegal(i+x,n))ans[i+x]='0';
                }

            }
            boolean w=true;
            for(int i=0;i<n;i++)
            {
                if(c[i]=='1')
                {
                    if(islegal(i-x,n)&& ans[i-x]=='1')continue;

                    if(islegal(i+x,n)&& ans[i+x]=='1')continue;
                    w=false;

                }
            }
            String oo="";
            for(int i=0;i<n;i++)
            {
                oo+=ans[i];
            }




            if(w)
            sb.append(oo+"\n");
            else
                sb.append(-1+"\n");

        }
        System.out.println(sb);
    }
}
