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
import sys    
test= int(input())
for i in range(test):
    s=input()
    x=int(input())
    n= len(s)
    w= [0]*n
    for j in range(n):
        if(j-x)<0:
            if(j+x)<n:
                w[j]= int(s[j+x])
        elif (j+x)>=n :
            if(j-x)>=0:
                w[j]= int(s[j-x])
        else:
            w[j]= int(s[j-x]) & int(s[j+x])

            
    
    flag=True
    for it in range(n):
        if(it-x)<0 and (it+x)>=n:
            if(s[it]=="1"):
                flag=False
                break                
            continue
        
        if(it-x)<0:
            if(int(s[it])!= w[it+x]):
                flag=False
                break
                    
        elif (it+x)>=n:
            if(int(s[it])!= w[it-x]):
                flag=False
                break
        else:
            if(int(s[it])!= (w[it-x] | w[it+x])):
                    flag=False
                    break
    #print(w)
    if(flag==True):
        ans=""
        for it in range(n):
            ans+= str(w[it])
        print(ans)
    else:
        print(-1)
        
        
        
   
      
    
    
