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
//Coded By Visnunathan

import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.lang.*;

public class codeforces {
    //static int[] arr;
    static int k,n;
    public static boolean isLegal(int x) {
        if(x >= 0 && x < n) return true;
        return false;
    }
    public static void main(String[] args) {
        FastScanner sc=new FastScanner();
        int T=sc.nextInt();
        for (int tt=0; tt<T; tt++) {
            char[] arr = sc.next().toCharArray();
            n = arr.length;
            int x = sc.nextInt();
            int[] str = new int[n];
            int f = 0;
            Arrays.fill(str,1);
            for(int i=0; i<n; i++) {
                if(arr[i] == '0') {
                    if(isLegal(i-x)) str[i-x] = 0;
                    if(isLegal(i+x)) str[i+x] = 0;
                }
            }
            for(int i=0; i<n; i++) {
                if(arr[i] == '1') {
                    if(isLegal(i-x) && str[i-x]==1) continue;
                    if(isLegal(i+x) && str[i+x]==1) continue;
                    f = 1;break;
                }
            }
            if(f == 1) System.out.println("-1");
            else{
                for(int i=0; i<n; i++) {
                    System.out.print(str[i]);
                }
                System.out.println();
            }
        }
    }

    static final Random random=new Random();
    
    static void ruffleSort(int[] a) {
        int n=a.length;//shuffle, then sort 
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n), temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }
    
    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }
        
        int nextInt() {
            return Integer.parseInt(next());
        }
        int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }

    
}
