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.Arrays;
import java.util.StringTokenizer;


public class Learning {
    public static void main(String[] args) throws Exception {
        StringBuilder st = new StringBuilder();
        FastInput in = new FastInput();
        int tt = in.nextInt();
        for (int t = 1; t <= tt; t++) {
            char[] s = in.next().toCharArray();
            int n = s.length;
            int x = in.nextInt();
            int[] c = new int[n];
            Arrays.fill(c, -1);
            boolean[] done = new boolean[n];
            for (int i = 0; i < n; i++) {
                if (i - x >= 0 && i + x < n) {
                    if (s[i - x] == s[i + x]) {
                        c[i] = s[i - x] - '0';
                        done[i - x] = done[i + x] = true;
                    } else if (s[i - x] == '0') {
                        c[i] = 0;
                        done[i - x] = true;
                    } else if (s[i + x] == '0') {
                        c[i] = 0;
                        done[i + x] = true;
                    }
                } else if (i - x >= 0) {
                    c[i] = s[i - x] - '0';
                    done[i - x] = true;
                } else if (i + x < n) {
                    c[i] = s[i + x] - '0';
                    done[i + x] = true;
                }
            }
            boolean f = false;
            for (int i = 0; i < n; i++) {
                if (!done[i]) {
                    if(s[i]=='1') {
                        if (i - x >= 0 && c[i - x] == -1) {
                            c[i - x] = s[i] - '0';
                            done[i] = true;
                            continue;
                        }
                        if (i + x < n && c[i + x] == -1) {
                            c[i + x] = s[i] - '0';
                            done[i] = true;
                            continue;
                        }
                        f = true;
                        break;
                    }
                }
            }
            if (f) {
                st.append(-1).append("\n");
                continue;
            }
            for (int i : c) {
                int p = i;
                if (i == -1) {
                    p = 1;
                }
                st.append(p);
            }
            st.append("\n");
        }
        System.out.print(st);

    }
}


class FastInput {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st;

    String next() throws IOException {
        if (st == null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    Integer nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    Long nextLong() throws IOException {
        return Long.parseLong(next());
    }
}