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.BufferedWriter;
import java.util.*;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStreamWriter;
import java.lang.reflect.Array;

//3
// CodeForces
public class Main {
	 
	public static void main (String[] args) throws java.lang.Exception {
		BufferedWriter log = new BufferedWriter(new OutputStreamWriter(System.out));
        InputReader in = new InputReader(System.in);
    	int T = in.readInt();
    	while(T-->0) {
    		String s = in.readString();
    		char [] w = new char[s.length()];
    		boolean flag = false;
    		Arrays.fill(w, '1');
    		int x = in.readInt();
    		int n = s.length();
    		for(int i = 0;i<s.length();i++) {
    			if(s.charAt(i)=='0') {
    				if(i>=x) w[i-x] = '0';
    				if(i<=s.length()-1-x) w[i+x] = '0';
    			}
    		}
    		for(int i = 0;i<w.length;i++) {
    			if(s.charAt(i)=='1') {
    				if(legal(i-x,n)&&w[i-x]=='1') continue;
    				if(legal(i+x,n)&&w[i+x]=='1') continue;
    				flag = true;
    			}
    		}
    		
    		if(flag) {
    			log.write(-1+"\n");
    		} else {
    			for(char t:w) {
    				log.write(t+"");
    			}
    			log.write("\n");
    		}
        	log.flush();
    	}
        
    }
	public static boolean legal(int x,int n) {
		return x>=0&&x<n;
	}
}

class InputReader {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;
    public InputReader(InputStream stream) {
        this.stream = stream;
    }
    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }
    public int readInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }
    public String readString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }
    public boolean isSpaceChar(int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
    public String next() {
        return readString();
    }
    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}
 
class IOUtils {
    public static int[] readIntArray(InputReader in, int size) {
        int[] array = new int[size];
        for (int i = 0; i < size; i++)
            array[i] = in.readInt();
        return array;
    }
}

