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())
for _ in range(t):
    s=input()
    x=int(input())
    
    w=[-1]*len(s)
    n=len(s)
    
    flag=0
    for i in range(0,n):
        if s[i]=="0":
            if i-x>=0:
                w[i-x]=0
            if i+x<n:
                w[i+x]=0
            
    
    for i in range(n):
        if s[i]=='1':
            if i-x>=0 and i+x<n:
                if w[i-x]==0 and w[i+x]==0:
                    flag=1
                    break
                if w[i-x]==0 and w[i+x]!=0:
                    w[i+x]=1
                elif w[i-x]!=0 and w[i+x]==0:
                    w[i-x]=1
                else:
                    w[i-x]=1
                    w[i+x]=1
            elif i-x>=0 and i+x>=n:
                if w[i-x]==0:
                    flag=1
                    break
                else:
                    w[i-x]=1
            elif i-x<0 and i+x<n:
                if w[i+x]==0:
                    flag=1
                    break
                else:
                    w[i+x]=1
            else:
                flag=1
                break
    
       # print(w)
    if flag==1:
        print(-1)
    else:
        for i in range(n):
            if w[i]==-1:
                w[i]=1
        
        for i in w:
            print(i,end="")
        print()
                
            
    
    