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
try:
    for i in range(int(input())):
        s=str(input())
        x=int(input())
        n=len(s)
        z=x
        st=''
        string=['1']*n
        for i in range(len(s)):
            if s[i]=='0':
                if i>=z:
                    string[i-z]='0'
                if i+z<len(s):
                    string[i+z]='0'
        for i in range(len(s)):
            if s[i]=='1':
                count1=0
                count2=0
                if i>=z and string[i-z]=='1':
                    count1+=1
                else:
                    count2+=1
                if i+z<len(s) and string[i+z]=='1':
                    count1+=1
                else:
                    count2+=1
                if count1==0:
                    string=['-1']
                    break
        for i in string:
            st+=i
        print(st)
except Exception as e:
    pass