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.Arrays;
import java.util.Scanner;

public class Contest94
{

	
	public static void main(String[] args)
	{
		Scanner s = new Scanner(System.in);
		int tc = s.nextInt();
		for (int t = 0; t < tc; t++)
		{
			String str = s.next();
			int x = s.nextInt();
			char []result = new char[str.length()];
			Arrays.fill(result, '1');
			boolean flag = true;
			for(int i=0; i<str.length(); i++)
			{
				if(str.charAt(i) == '0')
				{
					if(i-x >= 0)
					{
						result[i-x] = '0';
					}
					if(i+x < str.length())
					{
						result [i+x] = '0';
					}
				}
			}
			//System.out.println(new String(result));
			for(int i=0; i<str.length(); i++)
			{
				
				if(i-x >=0 && result[i-x]=='1' || i+x < str.length() && result[i+x] == '1')
				{
					if(str.charAt(i) != '1')
					{
						flag = false;
						//System.out.println("broke at i:"+i);
						break;
					}
				}
				else
				{
					if(str.charAt(i) == '1')
					{
						flag = false;
						//System.out.println("broke at i:"+i);
						break;
					}
				}
			}
			if(!flag)
			{
				System.out.println(-1);
			}
			else
				System.out.println(new String(result));
		}
	}
	
	public static void mainB(String[] args)
	{
		Scanner s = new Scanner(System.in);
		int tc = s.nextInt();
		for (int t = 0; t < tc; t++)
		{
			int p = s.nextInt();
			int f = s.nextInt();
			int cs = s.nextInt();
			int cw = s.nextInt();
			int sword = s.nextInt();
			int w = s.nextInt();
			int bigger = p<f?f:p;
			int totalw = p +f - bigger;
			int count = 0;

			for (int i = 0; i < 2; i++)
			{
				
				if (sword < w)
				{
					if (totalw < sword * cs)
					{
						count = totalw / sword;
						cs -= count;
						//System.out.println("1 :"+count);
					}
					else
					{
						count = cs + count;
						totalw = totalw - sword * cs;
						cs = 0;
						//System.out.println("2 :"+count);
						if (totalw > w * cw)
						{
							count = count + cw;
							cw = 0;
							//System.out.println("3 :"+count);
						}
						else
						{
							int cnt = totalw / w;
							count = count + cnt;
							cw = cw - cnt;

							//System.out.println("4 :"+count);
						}

					}
				}
				else
				{
					if (totalw < w * cw)
					{
						int cnt = totalw / w;
						count = count + cnt;
						cw = cw - cnt;
						//System.out.println("5 :"+count);
					}
					else
					{
						count = cw + count;
						totalw = totalw - w * cw;
						cw = 0;
						//System.out.println("6 :"+count);
						if (totalw > sword * cs)
						{
							count = cs + count;
							cs = 0;
							//System.out.println("7 :"+count);
						}
						else
						{
							int cnt = totalw / sword;
							count = count + cnt;
							cs = cs - cnt;
							//System.out.println("8 :"+count);
						}

					}
				}
				totalw = bigger;
			}

			//System.out.println(p+" "+f+" "+cs+" "+cw+" "+sword+" "+w+" "+totalw);

			System.out.println(count);

		}
	}

	public static void mainA(String[] args)
	{
		Scanner s = new Scanner(System.in);
		int tc = s.nextInt();
		for (int t = 0; t < tc; t++)
		{
			int n = s.nextInt();
			String str = s.next();
			String result = createString(n, "", str.charAt(n - 1));
			//System.out.println(result);

		}
	}

	public static String createString(int n, String s, char c)
	{
		if (s.length() == n)
			return s;
		else
		{
			String r = "";
			r = createString(n / 2, s, c);
			if (n % 2 == 0)
				r = r + r;
			else
				r = r + r + c;

			return r;

		}

	}
}
