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 stdout

def function(inp,x):
    output = []
    n = len(inp)

    for i in range(n):
        pre_in = 0
        if i >2*x-1:
            pre_in = inp[i-2*x]
        post_in = 0
        if i < n-2*x:
            post_in = inp[i+2*x]
        if inp[i] == "1" and (pre_in =="0" or i-x <0) and (post_in =="0" or i+x >=n):
            return "-1"
        pre_in = None
        if i >x-1:
            pre_in = inp[i-x]
        post_in = None
        if i < n-x:
            post_in = inp[i+x]
        #print(pre_in,post_in)
        if pre_in=="0"  or post_in=="0":
            output.append("0")
        else:
            output.append("1")


    return ''.join(output)


total = int(input())
inp = None
for index in range(2*total):
    line = input()
    if index % 2 == 0:
        inp = line
    else:
        x = int(line)
        result = function(inp,x)
        print(result)

    stdout.flush()