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.InputStreamReader;
import java.util.StringTokenizer;
import java.util.function.Function;

public class Main {

    public static void main(String[] args) {

        Parser parser = new Parser();
        int t = parser.parseInt();
        for (int i = 1; i <= t; i++) {
            Problem problem = new Problem();
            problem.solve(i);
        }
    }
}

class Problem {

    Parser parser = new Parser();

    public void solve(int testNum) {
        char[] s = parser.parseString().toCharArray();
        int x = parser.parseInt();

        int len = s.length;
        char[] ans = new char[len];
        for(int i = 0; i < len; i++) {
            if(i + x < len && s[i] == '0') {
                ans[i + x] = '0';
            }
            if(i - x >= 0 && s[i] == '0') {
                ans[i - x] = '0';
            }
        }

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

        char[] diff = new char[len];
        for(int i = 0; i < len; i++) {
            if(i - x >= 0 && ans[i - x] == '1') {
                diff[i] = '1';
            } else if(i + x < len && ans[i + x] == '1') {
                diff[i] = '1';
            } else {
                diff[i] = '0';
            }
            if(s[i] != diff[i]) {
                System.out.println(-1);
                return;
            }
        }

        StringBuilder sb = new StringBuilder();
        System.out.println(sb.append(ans).toString());
    }
}

class MathUtil {

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

    public static long pow(long x, long y) {
        return pow(x, y, Function.identity());
    }

    public static long pow(long x, long y, long mod) {
        return pow(x, y, v -> v % mod);
    }

    private static long pow(long x, long y, Function<Long, Long> action) {
        long res = 1;
        long t = x;
        while (y > 0) {
            if ((y & 1) == 1) {
                res += t;
                res = action.apply(res);
            }
            t *= t;
            t = action.apply(t);
            y /= 2;
        }
        return res;
    }
}

class DisjointSet {

    private final int[] f;

    public DisjointSet(int size) {
        f = new int[size + 1];
        for (int i = 0; i <= size; i++) {
            f[i] = i;
        }
    }

    public int find(int u) {
        if (f[u] == u) return u;
        return f[u] = find(f[u]);
    }

    public boolean merge(int u, int v) {
        u = find(u);
        v = find(v);
        if (u == v) return false;
        if (u > v) {
            int t = u;
            u = v;
            v = t;
        }
        f[u] = v;
        return true;
    }
}

class Parser {
    private static final BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    private StringTokenizer tokenizer;

    void fill() {
        while (tokenizer == null || !tokenizer.hasMoreElements()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
    }

    int parseInt() {
        fill();
        return Integer.parseInt(tokenizer.nextToken());
    }

    long parseLong() {
        fill();
        return Long.parseLong(tokenizer.nextToken());
    }

    double parseDouble() {
        fill();
        return Double.parseDouble(tokenizer.nextToken());
    }

    String parseString() {
        fill();
        return tokenizer.nextToken();
    }
}