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
from sys import stdin, stdout
t=int(stdin.readline())
for _ in range(t):
    arr=stdin.readline()
    arr=arr[:len(arr)-1]
    w=int(stdin.readline())
    n=len(arr)
    pc=[1]*n
    counter=0
    for i in range(n):

        if counter==1:
            break
        if arr[i]=='0':
            if i-w>=0:
                pc[i-w]=0
            if i+w<n:
                pc[i+w]=0
    nc=[i for i in pc]
    for i in range(n):
        c1,c2=0,0
        if i+w<n and i-w>=0 and pc[i+w]==1 and pc[i-w]==1:
            nc[i]=1
        elif (i+w<n and pc[i+w]==1) or (i-w>=0 and pc[i-w]==1):
            nc[i]=1
        else:
            nc[i]=0
        if int(arr[i])!=nc[i]:
            print(-1)
            counter=1
            break
    if counter==0:
        for i in range(n):
            print(pc[i],end='')

    print()



