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
def solve(string, x):
    n = len(string)
    possible = [{0: True, 1: True} for i in range(n)]
    for i in range(n):
        if string[i] == "0":
            if i >= x:
                possible[i - x][1] = False
            if i + x < n:
                possible[i + x][1] = False
        else:
            if i < x and i+x >= n:
                return -1
            elif i < x:
                possible[i+x][0] = False
            elif i + x >= n:
                possible[i-x][0] = False
            else:
                if not possible[i-x][1] and not possible[i+x][1]:
                    return -1
                elif not possible[i-x][1]:
                    possible[i+x][0] = False
                elif not possible[i+x][1]:
                    possible[i-x][0] = False

    output = ""
    for p in possible:
        if not p[0] and not p[1]:
            return -1
        elif not p[0]:
            output += "1"
        elif not p[1]:
            output += "0"
        else:
            output += "1"
                    
    return output

def main():
    t = int(input())
    for _ in range(t):
        string = input()
        x = int(input())

        answer = solve(string, x)
        print(answer)

main()