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.util.*;
import java.io.*;
 public class Codechef{
    public static void main(String []args) throws Exception{
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
   int tc=Integer.parseInt(br.readLine());
   while(tc-->0){
    String str=br.readLine();
    int x=Integer.parseInt(br.readLine());
    int n=str.length();
    int[] a=new int[n];
    Arrays.fill(a,1);
    boolean flag=true;
    for(int i=0;i<n;i++){
        if(str.charAt(i)=='0'){
            if(i-x>=0) a[i-x]=0;
            if(i+x<n) a[i+x]=0;
        }
    }
    for(int i=0;i<n;i++){
        if(str.charAt(i)=='1'){
           if(i-x>=0 && a[i-x]==1 || i+x<n && a[i+x]==1) continue;
           else{
               flag=false;
               break;
           }
        }
    }
    StringBuilder ans=new StringBuilder();
    for(int i:a) ans.append(i);
    if(flag) System.out.println(ans);
    else System.out.println("-1");
    }
 }
 }