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.*;
public class A{
    static PrintWriter out;
    static InputReader in;
    public static void main(String args[]){
        out = new PrintWriter(System.out);
        in = new InputReader();
        new A();
        out.flush(); out.close();
    }   
    A(){
        solve();
    }
    void solve(){
    	int test = in.nextInt();
    	while(test-- > 0){
    		char c[] = in.next().trim().toCharArray();
    		int x = in.nextInt(), l = c.length;
    		char ans[] = new char[l];
    		Arrays.fill(ans, '1');
    		for(int i = 0; i < l; i++){
    			if(c[i] == '0'){
    				if(i - x >= 0)ans[i - x] = '0';
    				if(i + x < l)ans[i + x] = '0';
    			} 
    		}
    		boolean rs = true;
    		for(int i = 0; i < l && rs; i++){
    			if(c[i] == '1'){
    				if(!((i - x >= 0 && ans[i - x] == '1') || (i + x < l && ans[i + x] == '1')))rs = false;
    			}
    		}
    		if(!rs)out.println(-1);
    		else{
    			for(int i = 0; i < l; i++)out.print(ans[i]);
    			out.println();
    		}
    	}
    }
    public static class InputReader{
        BufferedReader br;
        StringTokenizer st;
        InputReader(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        public int nextInt(){
            return Integer.parseInt(next());
        }
        public long nextLong(){
            return Long.parseLong(next());
        }
        public double nextDouble(){
            return Double.parseDouble(next());
        }
        public String next(){
            while(st == null || !st.hasMoreTokens()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch(IOException e){}
            }
            return st.nextToken();
        }
    }
}
	