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
def check_strings(string,string2,k):
    result=True
    for index in range(len(string2)):
        selected_char=int(string[index])
        left_char=None
        right_char=None
        char_to_use=0
        if index-k>=0:
            left_char=string2[index-k]
        if index+k<len(string):
            right_char=string2[index+k]
        if (left_char!=None and left_char==1) or (right_char!=None and right_char==1):
            char_to_use=1

        if selected_char!=char_to_use:
            result=False
            break
    return result


def make_string(string,k):
    result=-1
    new_string=[]
    for elem in string:
        new_string.append(1)

    for index in range(len(string)):
        elem=int(string[index])
        if elem==0:
            left_index=index-k
            right_index=index+k
            if left_index>=0:
                new_string[left_index]=0
            if right_index<len(string):
                new_string[right_index]=0

    cres=check_strings(string,new_string,k)
    if cres==True:
        for index in range(len(new_string)):
            digit=new_string[index]
            new_string[index]=str(digit)
        result="".join(new_string)
    return result


ammount=int(input())
for index in range(ammount):
    string=str(input())
    k=int(input())
    cres=make_string(string,k)
    print(cres)
