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;

public class C94 {
    static BufferedReader br;

    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        int t = readInt();
        while(t-->0){
            String str = br.readLine();
            StringBuilder s = new StringBuilder(str);
            int x = readInt();
            for(int i = 0; i < str.length(); i++)s.setCharAt(i, '1');
            for(int i = 0; i < str.length(); i++){
                if(str.charAt(i)=='0'){
                    if(i-x>=0)
                    s.setCharAt(i - x, '0');
                    if(i+x<str.length()){
                        s.setCharAt(i + x, '0');
                    }
                }
            }
            boolean flag = true;
            for(int i = 0; flag && i < str.length(); i++){
                if(str.charAt(i)=='1'){
                    boolean a = false;
                    if(i-x>=0 && s.charAt(i-x)=='0'){
                        a = true;
                    }
                    if(i-x<0){
                        a = true;
                    }
                    boolean b = false;

                    if(i+x>=s.length()){
                       b = true;
                    }
                    if(i+x<s.length() && s.charAt(i+x)=='0'){
                        b = true;
                    }
                    if(a && b){
                        flag = false;
                        System.out.println("-1");
                    }
                }
            }
            if(flag){
                System.out.println(s.toString());
            }
        }
    }

    static int readInt() throws IOException {
        return Integer.parseInt(br.readLine());
    }

    static long readLong() throws IOException {
        return Long.parseLong(br.readLine());
    }

    static long[] readLongarray() throws IOException {
        String[] _arr_ = br.readLine().split(" ");
        long[] a = new long[_arr_.length];
        for (int i = 0; i < _arr_.length; i++) {
            a[i] = Long.parseLong(_arr_[i]);
        }
        return a;
    }

    static int[] readIntarray() throws IOException {
        String[] _arr_ = br.readLine().split(" ");
        int[] a = new int[_arr_.length];
        for (int i = 0; i < _arr_.length; i++) {
            a[i] = Integer.parseInt(_arr_[i]);
        }
        return a;
    }
}
