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.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
 
public class ProblemC {
	public static void main(String[] args) throws IOException {
		InputStream in = System.in;
		InputReader scan = new InputReader(in);
		int test = scan.nextInt();
		StringBuilder sb = new StringBuilder();
		for(int t=0;t<test;t++) {
			String str = scan.next();
			int n = str.length();
			int x = scan.nextInt();
			int[] arr=new int[n];
			for(int i=0;i<n;i++) {
				arr[i] = -1;
			}
			for(int i=0;i<n;i++) {
				if(str.charAt(i)=='0') {
					if(i-x>=0) {
						arr[i-x]=0;
					}
					if(i+x<=n-1) {
						arr[i+x]=0;
					}
				}
			}
			boolean possible = true;
			for(int i=0;i<n;i++) {
				if(str.charAt(i)=='1') {
					boolean temp1 = true;
					boolean temp2 = true;
					if(i-x>=0) {
						if(arr[i-x]!=0) {
							arr[i-x]=1;
						} else {
							temp1 = false;
						}
					} else {
						temp1 = false;
					}
					if(i+x<=n-1) {
						if(arr[i+x]!=0) {
							arr[i+x]=1;
						} else {
							temp2 = false;
						}
					} else {
						temp2 = false;
					}
					if(!(temp1 || temp2)) {
						possible = false;
						break;
					}
				}
			}
			if(possible) {
				for(int i=0;i<n;i++) {
					if(arr[i]==-1) {
						sb.append(1);
					} else {
						sb.append(arr[i]);
					}
				}
			} else {
				sb.append(-1);
			}
			sb.append("\n");
		}
		System.out.print(sb);
 	}
	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;
 
		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}
 
		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}
 
		public int nextInt() {
			return Integer.parseInt(next());
		}
		
		public long nextLong() {
			return Long.parseLong(next());
		}
	}
}
