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):
    flag = True
    w=str(input())
    x=int(input())
    s= [-1] * len(w)

    for (i,ch) in enumerate(w):
        if(ch == '0'):
            if(i-x >= 0):
                s[i-x]= 0
            if(i+x < len(w)):
                s[i + x] = 0

    for(i,ch) in enumerate(w):
        if(ch == '1'):
            if(i-x < 0 and i+x < len(w)):
                if(s[i+x] == 0):
                    flag=0
                    break
                else:
                    s[i+x]=1
            elif(i - x >= 0 and i + x >= len(w)):
                if (s[i - x] == 0):
                    flag = 0
                    break
                else:
                    s[i - x] = 1
            elif(i-x >= 0 and i+x < len(w)):

                if(s[i-x] == 0 and s[i+x] == 0):
                    flag=0
                    break
                elif(s[i-x] == 0):
                    s[i+x]=1
                elif(s[i+x] == 0):
                    s[i-x]=1
                else:
                    s[i+x]=1
                    s[i-x]=1


    for (i,ch) in enumerate(s):
        if(s[i] == -1 and w[i] =='1'):
            flag=0


    if(flag == False):
        print(-1)
    else:
        for i  in s:
            if(i == -1):
                print(0,end='')
            else:
                print(i,end='')

        print(end = '\n')







