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.*;
import java.math.BigInteger;
import java.util.*;


public class gym{
	static void main() throws Exception{
		char[]in=sc.nextLine().toCharArray();
		int x=sc.nextInt();
		char[]ans=new char[in.length];
		Arrays.fill(ans, '7');
		for(int i=0;i<in.length;i++) {
			if(in[i]=='0') {
				if(i-x>=0 && i+x<in.length) {
					if(ans[i-x]=='1') {
						pw.println(-1);
						return;
					}
					ans[i-x]='0';
					if(ans[i+x]=='1') {
						pw.println(-1);
						return;
					}
					ans[i+x]='0';
				}
				else {
					if(i-x>=0) {
						if(ans[i-x]=='1') {
							pw.println(-1);
							return;
						}
						ans[i-x]='0';
					}
					else {
						if(i+x<in.length) {
							if(ans[i+x]=='1') {
								pw.println(-1);
								return;
							}
							ans[i+x]='0';
						}
					}
				}
			}
			
			else {
				//1
				if(i-x>=0 && i+x<in.length) {
					
				}
				else {
					if(i-x>=0) {
						if(ans[i-x]=='0') {
							pw.println(-1);
							return;
						}
						ans[i-x]='1';
					}
					else {
						if(i+x<in.length) {
							if(ans[i+x]=='0') {
								pw.println(-1);
								return;
							}
							ans[i+x]='1';
						}
					}
				}
			}
		}
		for(int i=0;i<in.length;i++) {
			if(ans[i]=='7') {
				ans[i]='1';
			}
		}
		for(int i=0;i<in.length;i++) {
			if(i-x>=0 && i+x<in.length) {
				if(ans[i-x]!='1' && ans[i+x]!='1') {
					if(in[i]!='0') {
						pw.println(-1);
						return;
					}
				}
				else {
					if(in[i]!='1') {
						pw.println(-1);
						return;
					}
				}
			}
			else {
				if(i-x>=0) {
					if(ans[i-x]!=in[i]) {
						pw.println(-1);
						return;
					}
				}
				else {
					if(i+x<in.length) {
						if(ans[i+x]!=in[i]) {
							pw.println(-1);
							return;
						}
					}
					else {
						if(in[i]!='0') {
							pw.println(-1);
							return;
						}
					}
				}
			}
		}
		
		for(int i=0;i<in.length;i++)pw.print(ans[i]);
		pw.println();
	}
	public static void main(String[] args) throws Exception{
		sc=new MScanner(System.in);
		pw=new PrintWriter(System.out);
		int tc=1;
		tc=sc.nextInt();
		while(tc-->0)
			main();
		pw.flush();
	}
	static PrintWriter pw;
	static MScanner  sc;
	static class MScanner {
		StringTokenizer st;
		BufferedReader br;
		public MScanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
 
		public MScanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int[] intArr(int n) throws IOException {
	        int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        return in;
		}
		public long[] longArr(int n) throws IOException {
	        long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        return in;
		}
		public int[] intSortedArr(int n) throws IOException {
	        int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        shuffle(in);
	        Arrays.sort(in);
	        return in;
		}
		public long[] longSortedArr(int n) throws IOException {
	        long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        shuffle(in);
	        Arrays.sort(in);
	        return in;
		}
		public Integer[] IntegerArr(int n) throws IOException {
	        Integer[]in=new Integer[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        return in;
		}
		public Long[] LongArr(int n) throws IOException {
	        Long[]in=new Long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        return in;
		}
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public char nextChar() throws IOException {
			return next().charAt(0);
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
 
		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
	static void shuffle(int[]in) {
		for(int i=0;i<in.length;i++) {
			int idx=(int)(Math.random()*in.length);
			int tmp=in[i];
			in[i]=in[idx];
			in[idx]=tmp;
		}
	}
	static void shuffle(long[]in) {
		for(int i=0;i<in.length;i++) {
			int idx=(int)(Math.random()*in.length);
			long tmp=in[i];
			in[i]=in[idx];
			in[idx]=tmp;
		}
	}
}