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.util.*;

import java.math.*;

public class Main {

	// static long sx = 0, sy = 0, mod = (long) (998244353);

	static ArrayList<Integer>[] a;
	static ArrayList<Long> p;
	// static Integer[][] dp;
	static HashMap<ArrayList<Integer>, Long> hm = new HashMap<>();
	static boolean[][] vis;
	static int[] farr;
	static long[] far;
	public static PrintWriter out = new PrintWriter(System.out);
	static ArrayList<pair> pa = new ArrayList<>();
	static long[] fact = new long[(int) 1e6];
	static StringBuilder sb = new StringBuilder();
	static boolean cycle = false;
	static long mo = (long) (1e9 + 7);
	// static int[] c, col;
	// static int n = 0, m, x, k;
	// static int ans = Integer.MAX_VALUE;
	static boolean b = true;
	static boolean[] reach = new boolean[6000];
	static int[][] par;
	static int[] depth;
	static int[] size;
	static long[] pow;
	static int time = 0;
	static int[] disc;
	static int[] low;
	static char[][] ch;
	// static int cnt = 0;
	static int[][] dirs = { { -1, 0 }, { 0, 1 }, { 1, 0 }, { 0, -1 }, };
	// static int n = 0, k = 0, z = 0;
	static long[] val;
	static String s1, s2;
	static long x, y;
	static int m = 0;
	static int n;
	static String str;
	static int odd, even;
	static long[] dp;
	static long[] dp1;
	static long[] col;
	static long ans;

	public static void main(String[] args) throws IOException {

		Scanner scn = new Scanner(new BufferedReader(new InputStreamReader(System.in)));

		// Reader scn = new Reader();

		int t = scn.nextInt();

		z: while (t-- != 0) {
			String s = scn.next();
			int x = scn.nextInt();
			int n = s.length();

			char[] w = new char[s.length()];

			for (int i = 0; i < s.length(); i++) {

				if (s.charAt(i) == '0') {

					if (i - x >= 0)
						w[i - x] = '0';
					if (i + x < n)
						w[i + x] = '0';
				}
			}

			for (int i = 0; i < s.length(); i++) {

				if (s.charAt(i) == '1') {

					boolean b = false;

					if (i - x >= 0 && w[i - x] != '0') {
						b = true;
						w[i - x] = '1';
					}

					if (i + x < n && w[i + x] != '0') {
						b = true;
						w[i + x] = '1';
					}

					if (!b) {
						System.out.println(-1);
						continue z;
					}
				}
			}

//			System.out.println(new String(w));
			for (int i = 0; i < n; i++)
				if (w[i] != '0' && w[i] != '1')
					w[i] = '0';

			System.out.println(new String(w));
		}
	}

	// _________________________TEMPLATE_____________________________________________________________

	// public static long lcm(long x, long y) {
	//
	// return (x * y) / gcd(x, y);
	// }
	//
	// private static long gcd(long x, long y) {
	// if (x == 0)
	// return y;
	//
	// return gcd(y % x, x);
	// }

	//
	// static class comp implements Comparator<Integer> {
	//
	// @Override
	// public int compare(Integer p1, Integer p2) {
	//
	// return p2 - p1;
	//
	// }
	// }
	//
	// }
	//
	// public static long pow(long a, long b, long mod) {
	//
	// if (b < 0)
	// return 0;
	// if (b == 0 || b == 1)
	// return (long) Math.pow(a, b);
	//
	// if (b % 2 == 0) {
	//
	// long ret = pow(a, b / 2, mod);
	// ret = (ret % mod * ret % mod) % mod;
	// return ret;
	// }
	//
	// else {
	// return ((pow(a, b - 1, mod) % mod) * a % mod) % mod;
	// }
	// }

	private static class pair implements Comparable<pair> {

		int i;
		int j;
		int cnt;

		pair(int a, int b, int c) {
			i = a;
			j = b;
			cnt = c;
		}

		@Override
		public int compareTo(pair o) {

			return this.cnt - o.cnt;
		}

		// @Override
		//
		// public int hashCode() {
		// return i;
		// }
		//
		// @Override
		//
		// public boolean equals(Object o) {
		//
		// pair p = (pair) o;
		// return this.i == p.i;
		// }

	}

	private static class pair1 {

		int a, b;

		pair1(int a, int b) {
			this.a = a;
			this.b = b;
		}

	}

	private static String reverse(String s) {

		return new StringBuilder(s).reverse().toString();
	}

	public static class Reader {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;

		public Reader() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public Reader(String file_name) throws IOException {
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String readLine() throws IOException {
			byte[] buf = new byte[1000000 + 1]; // line length
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}

		public int nextInt() throws IOException {
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}

		public long nextLong() throws IOException {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}

		public double nextDouble() throws IOException {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();

			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (c == '.') {
				while ((c = read()) >= '0' && c <= '9') {
					ret += (c - '0') / (div *= 10);
				}
			}

			if (neg)
				return -ret;
			return ret;
		}

		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}

		private byte read() throws IOException {
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}

		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}

		public int[] nextIntArray(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n) throws IOException {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}
			return arr;
		}

		public int[][] nextInt2DArray(int m, int n) throws IOException {
			int[][] arr = new int[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}

		public long[][] nextInt2DArrayL(int m, int n) throws IOException {
			long[][] arr = new long[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}
		// kickstart - Solution
		// atcoder - Main
	}

}