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
for _ in range(int(stdin.readline())):
    string = stdin.readline().strip()
    x = int(stdin.readline())
    build = ""
    flag = True
    array = [0] * len(string)
    if x + x > len(string):
        for i in range(len(string) - x):
            array[i + x] = string[i]
        for i in range(len(string) - x, x):
            if string[i] != "0":
                flag = False
            else:
                array[i] = "0"
        for i in range(x, len(string)):
            array[i - x] = string[i]
        if flag == False:
            print(-1)
        else:
            print("".join(array))
    else:
        for i in range(x):
            array[i + x] = string[i]
        for i in range(x, len(string) - x):
            if array[i - x] == 0:
                array[i - x] = string[i]
                if string[i] == "0":
                    array[i + x] = "0"
            else:
                if string[i] == "0":
                    if array[i - x] == "0":
                        array[i + x] = "0"
                    else:
                        if array[i - x] == 0:
                            array[i - x] = "0"
                            array[i + x] = "0"
                        else:
                            flag = False
                else:
                    if array[i - x] == "1":
                        pass
                    else:
                        if array[i - x] == "0":
                            array[i + x] = "1"
            if i + x + x >= len(string):
                array[i + x] = string[i]
        for i in range(len(string) - x, len(string)):
            if array[i - x] == 0:
                array[i - x] = string[i]
            if string[i] != array[i - x]:
                flag = False
        if flag:
            print("".join(array))
        else:
            print(-1)