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 i in range(int(input())):
    
    s=list(str(input()))
    x=int(input())
    ss="1"*(len(s))

    s=list(s)
    
    
    ss=list(ss)
   
 
    for i in range(len(s)):
   
        if s[i]=="0":
            
            if i-x >=0 and i-x<len(s):
                ss[i-x]="0"
            if i+x<=len(s)-1 and i+x>=0:
                ss[i+x]="0"

    wo=True
    for i in range(len(ss)):
        if s[i]=="1":
            if i-x >=0 and i-x<len(s) and ss[i-x]=="1":
                continue
            if i+x<len(s) and i+x>=0 and ss[i+x]=="1":
                continue
            wo=False
        
            
  
    

  
    
    if wo:
        an="".join(ss)
        print(an)
    else:
        print(-1)
            
              

