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 _ in range(int(input())):
    s=[x for x in input()]
    h=s.copy()
    n=int(input())
    dicti={}
    come=0
    for i in range(len(s)):
        if(s[i]=='0'):
            if(i<n and i>len(s)-n-1):
                continue
            elif(i<n):
                h[i+n]='0'
                if(i+n not in dicti):
                    dicti[i+n]=0
            elif(i>len(s)-n-1):
                h[i-n]='0'
                if(i-n not in dicti):
                    dicti[i-n]=0
            else:
                h[i-n]='0'
                h[i+n]='0'
                if(i+n not in dicti):
                    dicti[i+n]=0
                if(i-n not in dicti):
                    dicti[i-n]=0
    for i in range(len(s)):
        if(s[i]=='1'):
            if(i<n and i>len(s)-1-n):
                come=1
                break
            elif(i<n):
                if(i+n in dicti):
                    come=1
                    break
                else:
                    h[i+n]='1'
            elif(i>len(s)-1-n):
                if(i-n in dicti):
                    come=1
                    break
                else:
                    h[i-n]='1'
            else:
                if((i-n in dicti) and (i+n in dicti)):
                    come=1
                    break
                elif(i-n in dicti):
                    h[i+n]='1'
                elif(i+n in dicti):
                    h[i-n]='1'
                else:
                    h[i-n]='1'
                    h[i+n]='1'
                
    if(come==1):
        print(-1)
    else:
        hh=''
        print(hh.join(h))
                
                
                
            
            