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
if __name__ == "__main__":
    for _ in range(int(input())):
        # Input provided
        string = list(input())
        x = int(input())
        len_str = len(string)
        # declare all the values in w == 1
        w = ['1' for _ in range(len_str)]
        # formation of w
        for ind, s in enumerate(string):
            if s == '0':
                if (ind) - x >= 0:
                    w[(ind) - x] = '0'
                if (ind) + x < len_str:
                    w[(ind) + x] = '0'
        # verification of w
        # print(w)
        test = ['0' for _ in range(len_str)]
        for ind in range(0, len_str):
            if (ind + x) < len_str:
                if w[ind + x] == '1':
                    test[ind] = '1'
                    continue
            if (ind - x) >= 0:
                if w[ind - x] == '1':
                    test[ind] = '1'
                    continue
        # print(test)
        # print(test, string)
        if test == string:
            print(''.join(w))
        else:
            print(-1)
