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 cf;
import java.io.*;
import java.util.*;
public class c_94 {
    static int p=1000000007;
    public static void main(String[] args) throws Exception{
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(java.io.FileDescriptor.out), "ASCII"), 512);
        FastReader sc=new FastReader();
        // long k = sc.nextLong();
        StringBuilder ret=new StringBuilder();
        int t=sc.nextInt();
        while(t-->0) {
            char s[]=sc.nextLine().toCharArray();
            int res[]=new int [s.length];
            int x= sc.nextInt();
            int n=s.length;
            Arrays.fill(res,1);
            for(int i=0;i<s.length;i++)
            {
                if(s[i]=='0')
                {
                    if(i+x<n)
                    {
                        res[i+x]=0;
                    }
                    if(i-x>=0)
                        res[i-x]=0;

                }
            }
            int f=0;
        //    System.out.println(Arrays.toString(res));
        //   System.out.println(Arrays.toString(s));
            for(int i=0;i<s.length;i++) {
                if(s[i]=='1')
                {
                    f=1;
                    if(i+x<n&&res[i+x]==1) {
                        f=0;
                    }if(i-x>=0&&res[i-x]==1)
                    {
                        f=0;
                    }
                    if(f==1)
                        break;
                }

            }
            StringBuilder tem=new StringBuilder();
            if(f!=1)
            {
                for(int i:res)
                {
                    tem.append(i);
                }
            }

            if(f==1)
                ret.append("-1\n");
            else
                ret.append(tem.toString()+"\n");
            }
        System.out.println(ret.toString());
//        out.write(sb.toString());
        out.flush();
    }
    public static int toggle(int n,int k)
    {
        int t=((n>>k&1)<<k);
        System.out.println("t"+ t);
        if(t>0)
            n=n&~t;
        else
        {
            t=1<<k;
            n=n|t;
        }
        return n;
    }






    ///////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////
    static class FastReader {

        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }


}
