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
"""
NTC here
"""


def iin(): return int(input())


def lin(): return list(map(int, input().split()))


def main():
    T = iin()
    while T:
        T -= 1
        s = list(map(int, input()))
        x = iin()
        n = len(s)
        w = [-1]*n
        for i in range(n):
            if not s[i]:
                if i+x < n:
                    w[i+x] = 0
                if i-x >= 0:
                    w[i-x] = 0
        br = 0
        # print('i2', w)
        for i in range(n):
            if s[i]:
                ch = 0
                if i+x<n and w[i+x]==-1:
                    ch += 1
                if i-x>=0 and w[i-x]==-1:
                    ch += 1
                if ch:
                    pass
                else:
                    br = 1
                    break
                
        if br:
            print(-1)
            continue
        # print('i3', w)
        w = [i if i!=-1 else 1 for i in w]
        print(*w, sep='')



main()
