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 fun(s,x):
       n=len(s)
       ans=""
       for i in range(n):
              if((i-x>=0 and s[i-x]=='1') or (i+x<n and s[i+x]=='1')):
                  ans=ans+"1"
              else:
                  ans=ans+"0"   
       return ans  
t=int(input())                        
while(t>0):
   s=input()
   x=int(input())
   n=len(s)
   flag=0
   ans=['1' for _ in range(n)]
   for i in range(n):
      if(s[i]=='0'):
         if(i-x>=0):
            ans[i-x]='0'
         if(i+x<n):
            ans[i+x]='0'
   if(fun(ans,x)==s):
      print("".join(ans))
   else:
      print(-1)            
   
   t-=1   