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 main():
    line = list(input())
    n = len(line)
    copy = list("?"*n)
    x = int(input())
    for i in range(n):
        if i - x >= 0:
            if copy[i - x] == "?" or copy[i - x] == line[i]:
                copy[i - x] = line[i]
                if line[i] == "0" and i + x < n:
                    copy[i + x] = line[i]
            elif copy[i - x] != line[i]:
                if line[i] == "0":
                    print(-1)
                    return
                elif i + x < n:
                    if copy[i + x] == "?" or copy[i + x] == line[i]:
                        copy[i + x] = line[i]
                    else:
                        print(-1)
                        return
                else:
                    print(-1)
                    return
            else:
                return 0
        elif i + x < n:
            if copy[i + x] == "?" or copy[i + x] == line[i]:
                copy[i + x] = line[i]
            else:
                print(-1)
                return
        elif line[i] == "1":
            print(-1)
            return
    for i in range(n):
        if copy[i] == "?":
            copy[i] = "0"
    line = ""
    for i in copy:
        line += i
    print(line)

if __name__ == '__main__':
    t = int(input())
    for i in range(t):
        main()

"""
4 3 2 1
3 4 2 1 (1)
2 3 4 1 (3)
1 2 3 4 (6)
4 * 3 = 6 - 1 = 5
"""
