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 Equal {
    static class myInt implements Comparable<myInt> {
        int i;

        public myInt(int x) {
            i = x;
        }

        @Override
        public int compareTo(myInt o) {
            return o.i - i;
        }
    }


    public static void main(String[] args) throws IOException {
        //BufferedReader br = new BufferedReader(new FileReader("name.in"));
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;
        PrintWriter out = new PrintWriter(System.out);


        int T = Integer.parseInt(br.readLine());
        while (T-- > 0) {
           String s=br.readLine();
           int x=Integer.parseInt(br.readLine());
           char[]c=new char[s.length()];
           boolean valid=true;
           Arrays.fill(c,'a');
            for (int i = 0; i <s.length() ; i++) {
                if(s.charAt(i)=='1')
                    continue;
                if(i+x<c.length)
                    c[i+x]='0';
                if(i-x>=0)
                    c[i-x]='0';
            }
            for (int i = 0; i <s.length()&&valid ; i++) {
                if(s.charAt(i)=='0')
                    continue;
                if(i+x<s.length()){
                    if(c[i+x]!='0')
                        c[i+x]='1';
                    else{
                        if(i-x>=0){
                            if(c[i-x]!='0')
                                c[i-x]='1';
                            else valid=false;
                        }
                        else valid=false;
                    }
                }
                else {
                    if (i - x >= 0) {
                        if (c[i - x] != '0')
                            c[i - x] = '1';
                        else {
                            if (i + x < s.length()) {
                                if (c[i + x] != '0')
                                    c[i + x] = '1';
                                else valid = false;
                            } else valid = false;
                        }
                    }
                    else valid=false;
                }
            }
            if(!valid)
                out.println(-1);
            else{
                for (int i = 0; i <c.length ; i++) {
                    if(c[i]=='a')
                        c[i]='1';
                    out.print(c[i]);
                }
                out.println();
            }

        }
        out.flush();
        out.close();

    }


}
