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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.text.DateFormat;
import java.text.Format;
import java.text.ParseException;
import java.text.SimpleDateFormat;
import java.time.LocalDateTime;
import java.util.*;
import java.io.*;
import java.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.function.*;
import java.util.regex.*;
import java.util.stream.*;
import static java.util.stream.Collectors.joining;
import static java.util.stream.Collectors.toList;

public class file {



    private static final Scanner sc = new Scanner(System.in);
    private static String s;
    private static int[] arr;
    private static HashSet<Long> set;
    private static HashMap<Character, Integer> cmap;
    private static Map<Long, Long> Lmap;
    private static Map<Integer, Integer> map;
    private static Stack<Integer> stk;
    private static ArrayList<Integer>[] graph;
    private static boolean[] visited;
    private static ArrayList<Integer> list;
    private static ArrayList<Long> Llist;

    private static final int MOD = 1000000007;

    //find max of array
    private static int findMax(int[] arr) {
        int max = Integer.MIN_VALUE;
        for (int x : arr) {
            max = Math.max(x, max);
        }
        return max;
    }

    // print an array
    private static void printArray(int[] arr) {
        for (int x : arr) {
            System.out.print(x + " ");
        }
        System.out.println();
    }

    //DFS
    private static int dfs(int curr, int prev) {
        int count = 1;
        for (int next : graph[curr]) {
            if (next==prev) continue;
            long new_count = dfs(next, curr);
            Llist.add(new_count* (graph.length - new_count));
            count += new_count;
        }
        return count;
    }

    private static void foo(int testCase) {
        String s = sc.next();
        int x = sc.nextInt();
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < s.length(); i++) {
            sb.append('1');
        }
        for (int i = 0; i < s.length(); i++) {
            if (s.charAt(i) == '0') {
                if (i + x < s.length()) {
                    sb.setCharAt(i + x, '0');
                }
                if (i - x >= 0) {
                    sb.setCharAt(i - x, '0');
                }
            }
        }
        for (int i = 0; i < sb.length(); i++) {
            if (s.charAt(i) == '1') {
                if ((i + x < sb.length() ? sb.charAt(i + x) != '1' : true) && (i - x >= 0 ? sb.charAt(i - x) != '1' : true)) {
                    System.out.println(-1);
                    return;
                }

            }
        }
        System.out.println(sb.toString());
    }



    public static void main(String[] args) throws IOException {
        //foo(0);

        int t = sc.nextInt();
        for (int i = 0; i < t; i++) {
            foo(i);
        }

    }
}