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
for _ in range(int(input())):
     s = list(map(int,input()))
     x = int(input())
     #print(s)

     n = len(s)
     c = [1]*n
     for i in range(n):

          if s[i] == 0:
               if i -x >= 0:
                    c[i-x] = 0
               if i+ x < n:
                    c[i+x] = 0
                         
     flag = False
     for i in range(n):
          if s[i]== 1:
               if (i-x>=0 and c[i-x]==1) or (i+x<n and c[i+x]==1):
                    pass
               else:
                    flag = True
                    break
     if flag==True:
          print(-1)
     else:
          print(''.join(str(i) for i in c))

     
