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
 
t= int(input())
while(False):
    break
for i in range(t):
    s=input()
    n= len(s)
    xx=int(input())
    aa=1000
    while(False):
        break
    arrw= [0]*n
    for m in range(n):
        if(m-xx)<0:
            if(m+xx)<n:
                arrw[m]= int(s[m+xx])
        elif (m+xx)>=n :
            if(m-xx)>=0:
                arrw[m]= int(s[m-xx])
        else:
            while(False):
                break
            arrw[m]= int(s[m-xx]) & int(s[m+xx])

            
    while(False):
        break
    check=True
    for num in range(n):
        if(num-xx)<0 and (num+xx)>=n:
            if(s[num]=="1"):
                check=False
                break                
            continue
        aaa=100
        if(num-xx)<0:
            if(int(s[num])!= arrw[num+xx]):
                while(False):
                    break
                check=False
                break
                    
        elif (num+xx)>=n:
            if(int(s[num])!= arrw[num-xx]):
                check=False
                break
        else:
            if(int(s[num])!= (arrw[num-xx] | arrw[num+xx])):
                    check=False
                    break
    while(False):
        break
    if(check==True):
        disp=""
        for num in range(n):
            disp+= str(arrw[num])
        while(False):
            break
        print(disp)
    else:
        print(-1)
        
        
        
   
      
    
    
