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
/**
 * 22-10-2020
 * Created by Himanshu
 **/

import java.util.*;
import java.io.*;
import java.math.*;

public class C1400 {
    public static void main(String[] args) throws IOException {
        PrintWriter out = new PrintWriter(System.out);
        Reader s = new Reader();
        int t = s.i();
        while (t-- > 0) {
            String str = s.s();
            int x = s.i();
            int n = str.length();
            char [] arr = new char[n];
            Arrays.fill(arr,'-');
            for (int i=x;i<Math.min(2*x,n);i++) arr[i] = str.charAt(i-x);
            boolean ok = true;
            for (int i=n-x-1;i>=Math.max(0,n-2*x);i--) {
                if (arr[i] == '-') arr[i] = str.charAt(i+x);
                else if (arr[i] != str.charAt(i+x)) {
                    ok = false;
                    break;
                }
            }
            if (!ok) {
                out.println(-1);
                continue;
            }
            for (int i=x;i<n-x;i++) {
                if (str.charAt(i) == '0') {
                    if (arr[i+x] == '-') arr[i+x] = '0';
                    else if (arr[i+x] == '1') {
                        ok = false;
                        break;
                    }
                    if (arr[i-x] == '-') arr[i-x] = '0';
                    else if (arr[i-x] == '1') {
                        ok = false;
                        break;
                    }
                }
            }
            if (!ok) {
                out.println(-1);
                continue;
            }
            for (int i=0;i<n;i++) {
                if (arr[i] == '-') arr[i] = '1';
            }
            StringBuffer sb = new StringBuffer();
            for (int i=0;i<n;i++) {
                if (i-x < 0 && i+x >=n) {
                  sb.append('0');
                } else if (i-x < 0) {
                    sb.append(arr[i+x]);
                } else if (i+x >= n) {
                    sb.append(arr[i-x]);
                } else {
                    if (arr[i-x] == '1' || arr[i+x] == '1') sb.append('1');
                    else sb.append('0');
                }
            }
            if (sb.toString().compareTo(str) == 0) {
                for (int i=0;i<n;i++) {
                    out.print(arr[i]);
                }
                out.println();
            } else out.println(-1);
        }
        out.flush();
    }

    public static void shuffle(long[] arr) {
        int n = arr.length;
        Random rand = new Random();
        for (int i = 0; i < n; i++) {
            long temp = arr[i];
            int randomPos = i + rand.nextInt(n - i);
            arr[i] = arr[randomPos];
            arr[randomPos] = temp;
        }
    }

    private static int power(int a, int n) {
        int result = 1;
        while (n > 0) {
            if (n % 2 == 0) {
                a = (a * a);
                n /= 2;
            } else {
                result = (result * a);
                n--;
            }
        }
        return result;
    }

    private static long query(long[] tree, int in, int start, int end, int l, int r) {
        if (start >= l && r >= end) return tree[in];
        if (end < l || start > r) return 0;
        int mid = (start + end) / 2;
        long x = query(tree, 2 * in, start, mid, l, r);
        long y = query(tree, 2 * in + 1, mid + 1, end, l, r);
        return x + y;
    }

    private static void update(int[] arr, long[] tree, int in, int start, int end, int idx, int val) {
        if (start == end) {
            tree[in] = val;
            arr[idx] = val;
            return;
        }
        int mid = (start + end) / 2;
        if (idx > mid) update(arr, tree, 2 * in + 1, mid + 1, end, idx, val);
        else update(arr, tree, 2 * in, start, mid, idx, val);
        tree[in] = tree[2 * in] + tree[2 * in + 1];
    }

    private static void build(int[] arr, long[] tree, int in, int start, int end) {
        if (start == end) {
            tree[in] = arr[start];
            return;
        }
        int mid = (start + end) / 2;
        build(arr, tree, 2 * in, start, mid);
        build(arr, tree, 2 * in + 1, mid + 1, end);
        tree[in] = (tree[2 * in + 1] + tree[2 * in]);
    }

    private static int power(int a, int n, int p) {
        int result = 1;
        while (n > 0) {
            if (n % 2 == 0) {
                a = (a * a) % p;
                n /= 2;
            } else {
                result = (result * a) % p;
                n--;
            }
        }
        return result;
    }

    static class Reader {
        private InputStream mIs;
        private byte[] buf = new byte[1024];
        private int curChar, numChars;

        public Reader() {
            this(System.in);
        }

        public Reader(InputStream is) {
            mIs = is;
        }

        public int read() {
            if (numChars == -1) throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = mIs.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public String s() {
            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 long l() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long 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 int i() {
            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 double d() throws IOException {
            return Double.parseDouble(s());
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

        public int[] arr(int n) {
            int[] ret = new int[n];
            for (int i = 0; i < n; i++) {
                ret[i] = i();
            }
            return ret;
        }

        public long[] arrLong(int n) {
            long[] ret = new long[n];
            for (int i = 0; i < n; i++) {
                ret[i] = l();
            }
            return ret;
        }
    }
//    static class pairLong implements Comparator<pairLong> {
//        long first, second;
//
//        pairLong() {
//        }
//
//        pairLong(long first, long second) {
//            this.first = first;
//            this.second = second;
//        }
//
//        @Override
//        public int compare(pairLong p1, pairLong p2) {
//            if (p1.first == p2.first) {
//                if(p1.second > p2.second) return 1;
//                else return -1;
//            }
//            if(p1.first > p2.first) return 1;
//            else return -1;
//        }
//    }
//    static class pair implements Comparator<pair> {
//        int first, second;
//
//        pair() {
//        }
//
//        pair(int first, int second) {
//            this.first = first;
//            this.second = second;
//        }
//
//        @Override
//        public int compare(pair p1, pair p2) {
//            if (p1.first == p2.first) return p1.second - p2.second;
//            return p1.first - p2.first;
//        }
//    }
}

