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.BigDecimal;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Queue;
import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.util.Collections;
import java.io.InputStreamReader;
import java.util.logging.SimpleFormatter;


public class Main1 {






    public static void main(String[] args) {


        try {


            FastScanner in = new FastScanner();
            PrintWriter out = new PrintWriter(System.out);



            int t = in.nextInt() ;
            outer :    while (t-- > 0){

                char a[] = in.next().toCharArray() ;
                int n = a.length ;
                int x = in.nextInt();

                int ans[] = new int[n] ;
                Arrays.fill(ans , -1);

                for (int i = 0; i <n ; i++) {
                    if (a[i] == '1'){
                        boolean flag = false ;
                        if (i - x >= 0){
                            if (ans[i-x] == 0){
                             flag = true ;
                            }
                            else ans[i-x] = 1 ;
                        }
                          if (i+x <n){
                            if (ans[i+x] == 0 && flag){
                                System.out.println(-1);
                                continue outer;
                            }
                            if (flag || i-x < 0)
                              ans[i+x] = 1 ;

                        }

                          if (flag && i+x >= n){
                              System.out.println(-1);
                              continue outer;
                          }


                        else if ( i-x <0 && i+x >=n  ){
                            System.out.println(-1);
                            continue outer;
                        }
                    }
                    else {

                        if (i-x >=0){
                            if (ans[i-x] == 1){
                                System.out.println(-1);
                                continue outer;
                            }
                            ans[i-x] = 0 ;
                        }
                        if (i+x <n){
                            if (ans[i+x] == 1){
                                System.out.println(-1);
                                continue outer;
                            }
                            ans[i+x] = 0 ;
                        }


                    }
                }

                for (int i = 0; i <n ; i++) {
                    if (ans[i] == -1)
                        ans[i] = 1 ;
                }

                StringBuilder sb = new StringBuilder() ;
                for (int i = 0; i <n ; i++) {
                    sb.append(ans[i]) ;
                }
                System.out.println(sb);


            }














            out.flush();
            out.close();
        }
        catch (Exception e){
            return;
        }

    }

    static int findLCA(int a, int b, int par[][], int depth[]) {
        if (depth[a] > depth[b]) {
            a = a ^ b;
            b = a ^ b;
            a = a ^ b;
        }
        int diff = depth[b] - depth[a];
        for (int i = 19; i >= 0; i--) {
            if ((diff & (1 << i)) > 0) {
                b = par[b][i];
            }
        }
        if (a == b)
            return a;
        for (int i = 19; i >= 0; i--) {
            if (par[b][i] != par[a][i]) {
                b = par[b][i];
                a = par[a][i];
            }
        }
        return par[a][0];
    }

    static int gcd(int a, int b) {
        return (b == 0) ? a : gcd(b, a % b);
    }

    static void formArrayForBinaryLifting(int n, int par[][]) {
        for (int j = 1; j < 20; j++) {
            for (int i = 0; i < n; i++) {
                if (par[i][j - 1] == -1)
                    continue;
                par[i][j] = par[par[i][j - 1]][j - 1];
            }
        }
    }


    static void sort(int ar[]) {
        int n = ar.length;
        ArrayList<Integer> a = new ArrayList<>();
        for (int i = 0; i < n; i++)
            a.add(ar[i]);
        Collections.sort(a);
        for (int i = 0; i < n; i++)
            ar[i] = a.get(i);
    }

    static void sort1(long ar[]) {
        int n = ar.length;
        ArrayList<Long> a = new ArrayList<>();
        for (int i = 0; i < n; i++)
            a.add(ar[i]);
        Collections.sort(a);
        for (int i = 0; i < n; i++)
            ar[i] = a.get(i);
    }

    static long ncr(long n, long r, long mod) {
        if (r == 0)
            return 1;
        long val = ncr(n - 1, r - 1, mod);
        val = (n * val) % mod;
        val = (val * modInverse(r, mod)) % mod;
        return val;
    }

    static long fast_pow(long base, long n, long M) {
        if (n == 0)
            return 1;
        if (n == 1)
            return base % M;
        long halfn = fast_pow(base, n / 2, M);
        if (n % 2 == 0)
            return (halfn * halfn) % M;
        else
            return (((halfn * halfn) % M) * base) % M;
    }

    static long modInverse(long n, long M) {
        return fast_pow(n, M - 2, M);
    }


    private static int countDigits(long l) {
        if (l >= 1000000000000000000L) return 19;
        if (l >= 100000000000000000L) return 18;
        if (l >= 10000000000000000L) return 17;
        if (l >= 1000000000000000L) return 16;
        if (l >= 100000000000000L) return 15;
        if (l >= 10000000000000L) return 14;
        if (l >= 1000000000000L) return 13;
        if (l >= 100000000000L) return 12;
        if (l >= 10000000000L) return 11;
        if (l >= 1000000000L) return 10;
        if (l >= 100000000L) return 9;
        if (l >= 10000000L) return 8;
        if (l >= 1000000L) return 7;
        if (l >= 100000L) return 6;
        if (l >= 10000L) return 5;
        if (l >= 1000L) return 4;
        if (l >= 100L) return 3;
        if (l >= 10L) return 2;
        return 1;
    }


    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private static final int THRESHOLD = 32 << 10;
        private final Writer os;
        private StringBuilder cache = new StringBuilder(THRESHOLD * 2);

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        private void afterWrite() {
            if (cache.length() < THRESHOLD) {
                return;
            }
            flush();
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput append(long c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput append(String c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput println() {
            return append(System.lineSeparator());
        }

        public FastOutput flush() {
            try {
                //            boolean success = false;
                //            if (stringBuilderValueField != null) {
                //                try {
                //                    char[] value = (char[]) stringBuilderValueField.get(cache);
                //                    os.write(value, 0, cache.length());
                //                    success = true;
                //                } catch (Exception e) {
                //                }
                //            }
                //            if (!success) {
                os.append(cache);
                //            }
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }


    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }


        long nextLong() {
            return Long.parseLong(next());
        }
    }


}







