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 Codeforces
{
    public static void main(String args[])throws Exception
    {
        BufferedReader bu=new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb=new StringBuilder();
        int t=Integer.parseInt(bu.readLine());
        while(t-->0)
        {
            char s[]=bu.readLine().toCharArray();
            int n=s.length,x=Integer.parseInt(bu.readLine()),ans[]=new int[n],i;
            Arrays.fill(ans,-1);
            i=0;
            boolean pos=true;
            while(i-x<0)
            {
                if(s[i]=='0')
                {
                    if(i+x<n) ans[i+x]=0;
                    else ans[i]=0;
                }
                else
                {
                    if(i+x<n) ans[i+x]=1;
                    else {pos=false; break;}
                }
                i++;
            }
            if(!pos) {sb.append("-1\n"); continue;}
            int st=i;

            i=n-1;
            while(i+x>=n)
            {
                if(s[i]=='0')
                {
                    if(i-x>=0)
                    {
                        if(ans[i-x]==1) {pos=false; break;}
                        ans[i-x]=0;
                    }
                }
                else
                {
                    if(i-x>=0)
                    {
                        if(ans[i-x]==0) {pos=false; break;}
                        ans[i-x]=1;
                    }
                    else {pos=false; break;}
                }
                i--;
            }
            if(!pos) {sb.append("-1\n"); continue;}
            int en=i;

            for(i=st;i<=en;i++)
            if(s[i]=='0')
            {
                if(ans[i-x]==1 || ans[i+x]==1) {pos=false; break;}
                ans[i-x]=0;
                ans[i+x]=0;
            }
            else
            {
                if(ans[i-x]==0 && ans[i+x]==0) {pos=false; break;}
                if(ans[i-x]!=0) ans[i-x]=1;
                else ans[i+x]=1;
            }
            if(!pos) sb.append("-1\n");
            else
            {
                for(i=0;i<n;i++)
                if(ans[i]==-1) sb.append(0);
                else sb.append(ans[i]);
                sb.append("\n");
            }
        }
        System.out.print(sb);
    }
}