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 {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
    //class  Declaration
 
static class pair implements Comparable < pair > {
long x;
long y;
pair(long i, long j) {
    x = i;
    y = j;
}
public int compareTo(pair p) {
    if (this.x != p.x) {
        return Long.compare(this.x,p.x);
    } else {
        return Long.compare(this.y,p.y);
    }
}
public int hashCode() {
    return (x + " " + y).hashCode();
}
public String toString() {
    return x + " " + y;
}
public boolean equals(Object o) {
    pair x = (pair) o;
    return (x.x == this.x && x.y == this.y);
}
}

 
// int[] dx = {0,0,1,-1};
// int[] dy = {1,-1,0,0};
// int[] ddx = {0,0,1,-1,1,-1,1,-1}; 
// int[] ddy = {1,-1,0,0,1,-1,-1,1};
 
final int inf = (int) 1e9 + 9;
final long biginf  = (long)1e18 + 7 ;
final long mod =  (long)1e9+7;  

void solve() throws Exception {
int T=ni();
while(T-->0){
    char[] s = ns().toCharArray();
    int x= ni();
    int n=s.length;
    char[] w = new char[n];
    for(int i=0;i<n;++i){
        char set = s[i];
        boolean isZero = false ;
        if(i + x < n){
            if(s[i+x]=='0'){
                isZero = true ;
            }
        }
        if(i - x >= 0 ){
            if(s[i-x]=='0'){
                isZero = true;
            }
        }
        w[i] = (isZero?'0':'1');
    }  
    //watch(w);

    boolean pos = true ;
    for(int i=0;i<n;++i){
        if(s[i]=='0'){
            if( (i + x < n && w[i+x] != '0') || (i-x >=0 && w[i-x]!='0')){
                pos = false ;
                break ;
            }
        }
        else{
            boolean isOne = false ;
            if (i + x < n && w[i+x] == '1' ){
               isOne  = true ;
            }
            if (i - x >=0 && w[i-x] == '1' ){
                isOne  = true ;
            }
            if(!isOne){
                pos = false;
                break ;
            }
            
        }
    }
    if(pos){
        pn(new String(w));
    }   
    else pn(-1);

    


    
}
}



long pow(long a, long b) {
    long result = 1;
    while (b > 0) {
        if (b % 2 == 1) result = (result * a) % mod;
        b /= 2;
        a = (a * a) % mod;
    }
    return result;
}
 
void print(Object o) {
        System.out.println(o);
        System.out.flush();
}
long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
void run() throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
 
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        //System.out.println(System.currentTimeMillis() - s + "ms");
        if (!INPUT.isEmpty()) tr(System.currentTimeMillis() - s + "ms");
    }
 
 
public static void main(String[] args) throws Exception {
    new Main().run();
}
 
//output methods
private void pn(Object o) {
    out.println(o);
}
private void p(Object o) {
    out.print(o);
}
private ArrayList < ArrayList < Integer >> ng(int n, int e) {
    ArrayList < ArrayList < Integer >> g = new ArrayList < > ();
    for (int i = 0; i <= n; ++i) g.add(new ArrayList < > ());
 
    for (int i = 0; i < e; ++i) {
        int u = ni(), v = ni();
        g.get(u).add(v);
        g.get(v).add(u);
    }
 
    return g;
}
 
private ArrayList < ArrayList < pair >> nwg(int n, int e) {
    ArrayList < ArrayList < pair >> g = new ArrayList < > ();
    for (int i = 0; i <= n; ++i) g.add(new ArrayList < > ());
 
    for (int i = 0; i < e; ++i) {
        int u = ni(), v = ni(), w = ni();
        
        g.get(u).add(new pair(w, v));
        g.get(v).add(new pair(w, u));
    }
 
    return g;
}
 
 
//input methods
private byte[] inbuf = new byte[1024];
public int lenbuf = 0, ptrbuf = 0;
 
 
private int readByte() {
    if (lenbuf == -1) throw new InputMismatchException();
    if (ptrbuf >= lenbuf) {
        ptrbuf = 0;
        try {
            lenbuf = is.read(inbuf);
        } catch (IOException e) {
            throw new InputMismatchException();
        }
        if (lenbuf <= 0) return -1;
    }
    return inbuf[ptrbuf++];
}
 
 
 
 
private boolean isSpaceChar(int c) {
    return !(c >= 33 && c <= 126);
}
private int skip() {
    int b;
    while ((b = readByte()) != -1 && isSpaceChar(b));
    return b;
}
 
private double nd() {
    return Double.parseDouble(ns());
}
private char nc() {
    return (char) skip();
}
 
private String ns() {
    int b = skip();
    StringBuilder sb = new StringBuilder();
    while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
        sb.appendCodePoint(b);
        b = readByte();
    }
    return sb.toString();
}
 
private char[] ns(int n) {
    char[] buf = new char[n];
    int b = skip(), p = 0;
    while (p < n && !(isSpaceChar(b))) {
        buf[p++] = (char) b;
        b = readByte();
    }
    return n == p ? buf : Arrays.copyOf(buf, p);
}
 
private char[][] nm(int n, int m) {
    char[][] map = new char[n][];
    for (int i = 0; i < n; i++) map[i] = ns(m);
    return map;
}
 
private int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++) a[i] = ni();
    return a;
}
 
private int ni() {
    int num = 0, b;
    boolean minus = false;
    while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
    if (b == '-') {
        minus = true;
        b = readByte();
    }
 
    while (true) {
        if (b >= '0' && b <= '9') {
            num = num * 10 + (b - '0');
        } else {
            return minus ? -num : num;
        }
        b = readByte();
    }
}
 
private long nl() {
    long num = 0;
    int b;
    boolean minus = false;
    while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
    if (b == '-') {
        minus = true;
        b = readByte();
    }
 
    while (true) {
        if (b >= '0' && b <= '9') {
            num = num * 10 + (b - '0');
        } else {
            return minus ? -num : num;
        }
        b = readByte();
    }
}
 
private void tr(Object...o) {
    if (INPUT.length() > 0) System.out.println(Arrays.deepToString(o));
}
void watch(Object...a) throws Exception {
    int i = 1;
    print("watch starts :");
    for (Object o: a) {
        //print(o);
        boolean notfound = true;
        if (o.getClass().isArray()) {
 
            String type = o.getClass().getName().toString();
            //print("type is "+type);
            switch (type) {
                case "[I":
                    {
                        int[] test = (int[]) o;
                        print(i + " " + Arrays.toString(test));
                        break;
                    }
                case "[[I":
                    {
                        int[][] obj = (int[][]) o;
 
                        print(i + " " + Arrays.deepToString(obj));
                        break;
                    }
                case "[J":
                    {
 
                        long[] obj = (long[]) o;
                        print(i + " " + Arrays.toString(obj));
                        break;
                    }
                case "[[J":
                    {
 
                        long[][] obj = (long[][]) o;
                        print(i + " " + Arrays.deepToString(obj));
                        break;
                    }
                case "[D":
                    {
 
                        double[] obj = (double[]) o;
                        print(i + " " + Arrays.toString(obj));
                        break;
                    }
                case "[[D":
                    {
 
                        double[][] obj = (double[][]) o;
                        print(i + " " + Arrays.deepToString(obj));
                        break;
                    }
                case "[Ljava.lang.String":
                    {
 
                        String[] obj = (String[]) o;
                        print(i + " " + Arrays.toString(obj));
                        break;
                    }
                case "[[Ljava.lang.String":
                    {
 
                        String[][] obj = (String[][]) o;
                        print(i + " " + Arrays.deepToString(obj));
                        break;
                    }
                case "[C":
                    {
                        char[] obj = (char[]) o;
                        print(i + " " + Arrays.toString(obj));
                        break;
                    }
                case "[[C":
                    {
 
                        char[][] obj = (char[][]) o;
                        print(i + " " + Arrays.deepToString(obj));
                        break;
                    }
 
 
 
                default:
                    {
                        print(i + " type not identified");
                        break;
                    }
            }
            notfound = false;
 
        }
        if (o.getClass() == ArrayList.class) {
            print(i + " al: " + o);
            notfound = false;
        }
        if (o.getClass() == HashSet.class) {
            print(i + " hs: " + o);
            notfound = false;
        }
        if (o.getClass() == TreeSet.class) {
            print(i + " ts: " + o);
            notfound = false;
        }
        if (o.getClass() == TreeMap.class) {
            print(i + " tm: " + o);
            notfound = false;
        }
        if (o.getClass() == HashMap.class) {
            print(i + " hm: " + o);
            notfound = false;
        }
        if (o.getClass() == LinkedList.class) {
            print(i + " ll: " + o);
            notfound = false;
        }
        if (o.getClass() == PriorityQueue.class) {
            print(i + " pq : " + o);
            notfound = false;
        }
        if (o.getClass() == pair.class) {
            print(i + " pq : " + o);
            notfound = false;
        }
 
        if (notfound) {
            print(i + " unknown: " + o);
        }
        i++;
    }
    print("watch ends ");
}
 
}