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())
    n=len(s)
    w=[-1 for i in range(n)]

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

            elif (i+x>=n and i-x<0):
                flag=1
            
            else:
                if (w[i+x]==0 and w[i-x]==0):
                    flag=1
                    break

    if (flag==1):
        print(-1)

    else:
        ans=""
        for i in w:
            if (i==-1):
                ans=ans+"1"
            else:
                ans=ans+"0"
        print(ans)
        
