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 codeforces.div2;

import java.util.Scanner;

public class BinaryStringReconstruction {

    static public void print(String s, int w) {

        char arr[] = new char[s.length()];

        for(int i =0 ; i < arr.length; i++) {
            arr[i] = 'A';
        }
        boolean flag = false;
        for(int i = 0; i < s.length(); i++) {
            int val = s.charAt(i) - 48;
            if(val == 1) {
                if((i - w)>=0) {
                    if(arr[i-w] == 'A' || arr[i-w] == '1') {
                        arr[i-w] = '1';
                    } else {
                        if((i+w)<arr.length) {
                            if(arr[i+w] =='A' || arr[i+w] == '1') {
                                arr[i+w] = '1';
                            } else {
                                flag = true;
                            }
                        } else {
                            flag = true;
                        }
                    }
                } else {
                    if((i+w)<arr.length) {
                        if(arr[i+w] =='A' || arr[i+w] == '1') {
                            arr[i+w] = '1';
                        } else {
                            flag = true;
                        }
                    } else {
                        flag = true;
                    }
                }
            } else {
                if(i+w < arr.length) {
                   if(arr[i+w] == '1') {
                       flag = true;
                   }
                    arr[i+w] = '0';
                }
                if((i-w)>=0) {
                    if(arr[i-w] == '1') {
                        flag = true;
                    }
                    arr[i-w] = '0';
                }
            }
        }
        if(flag) {
            System.out.println("-1");
        } else {
            for(int i = 0; i < arr.length; i++) {
                if(arr[i] == 'A') {
                    arr[i] = '1';
                }
            }
            System.out.println(new String(arr));

        }
    }

    public static void main(String []args) {
        Scanner sc = new Scanner(System.in);
        int n  = sc.nextInt();
        while ( n > 0) {
            String s = sc.next();
            int w = sc.nextInt();
            print(s, w);
            n--;
        }
    }
}
