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.*;import java.math.*;
public class StringReconstruction
{
    public static void process()throws IOException
    {
        String s = nln();
        int x = ni();
        int n = s.length();
        int[] dp = new int[n+1];
        Arrays.fill(dp, 1);
        for(int i = 1; i <= n; i++){
            if(i+x <= n){
                if(s.charAt(i-1) == '0')
                    dp[i+x] = 0;
            }
            if(i-x > 0){
                if(s.charAt(i-1) == '0')
                    dp[i-x] = 0;
            }
        }
        int[] ns = new int[n+1];
        String str = "";
        for(int i = 1; i <= n; i++){
            if(i-x > 0){
                if(dp[i-x] == 1){
                    ns[i] = 1;
                }
            }
            if(i+x <= n){
                if(dp[i+x] == 1){
                    ns[i] = 1;
                }
            }
        }
        for(int i = 1; i <= n; i++)
            str = str+ns[i];
        //pn(str);
        //pn(s);
        if(str.equals(s)){
            for(int i = 1; i <= n; i++)
                p(dp[i]);
            pn("");
        }
        else
            pn(-1);
    }
   
    static AnotherReader sc;
    static PrintWriter out;
    public static void main(String[]args)throws IOException
    {
        boolean oj = System.getProperty("ONLINE_JUDGE") != null;
        if(oj){sc=new AnotherReader();out=new PrintWriter(System.out);}
        else{sc=new AnotherReader(100);out=new PrintWriter("output.txt");}
        long s = System.currentTimeMillis();
        int t=1;
        t=ni();
        while(t-->0) {process();}
        out.flush();
        System.err.println(System.currentTimeMillis()-s+"ms");
        out.close();
    }

 
    static void pn(Object o){out.println(o);}
    static void p(Object o){out.print(o);}
    static void pni(Object o){out.println(o);out.flush();}
    static int ni()throws IOException{return sc.nextInt();}
    static long nl()throws IOException{return sc.nextLong();}
    static double nd()throws IOException{return sc.nextDouble();}
    static String nln()throws IOException{return sc.nextLine();}
    static int[] nai(int N)throws IOException{int[]A=new int[N];for(int i=0;i!=N;i++){A[i]=ni();}return A;}
    static long[] nal(int N)throws IOException{long[]A=new long[N];for(int i=0;i!=N;i++){A[i]=nl();}return A;}
    static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));}
    static long power(long k, long c, long mod){
        long y = 1;
        while(c > 0){
            if(c%2 == 1)
                y = y * k % mod;
            c = c/2;
            k = k * k % mod;
        }
        return y;
    }
 
/////////////////////////////////////////////////////////////////////////////////////////////////////////
 
    static class AnotherReader{BufferedReader br; StringTokenizer st;
    AnotherReader()throws FileNotFoundException{
    br=new BufferedReader(new InputStreamReader(System.in));}
    AnotherReader(int a)throws FileNotFoundException{
    br = new BufferedReader(new FileReader("input.txt"));}
    String next()throws IOException{
    while (st == null || !st.hasMoreElements()) {try{
    st = new StringTokenizer(br.readLine());}
    catch (IOException  e){ e.printStackTrace(); }}
    return st.nextToken(); } int nextInt() throws IOException{
    return Integer.parseInt(next());}
    long nextLong() throws IOException
    {return Long.parseLong(next());}
    double nextDouble()throws IOException { return Double.parseDouble(next()); }
    String nextLine() throws IOException{ String str = ""; try{
    str = br.readLine();} catch (IOException e){
    e.printStackTrace();} return str;}}

/////////////////////////////////////////////////////////////////////////////////////////////////////////////
}