human
Give me a Python code to print the answer on a separate line as follows: given the following:
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
assistant
#Here is Python code to print the answer on a separate line as follows:
.

# class Conflict(Exception): pass

def controller(s, x):
    n = len(s)
    s = tuple(i=='1' for i in s)
    w = [None]*n
    constraints = []
    # def set(idx, val):
    #     oldval = w[idx]
    #     if oldval is None:
    #         w[idx] = val
    #     else:
    #         if oldval is val:
    #             pass
    #         else:
    #             raise Conflict()
    for i,si in enumerate(s):
        a = i-x
        b = i+x
        has_a = 0<=a
        has_b = b<n
        if has_a:
            if has_b:
                if si:
                    constraints.append(i)
                else:
                    # set(a, False)
                    # set(b, False)
                    if w[a] is None:
                        w[a] = False
                    elif w[a] is True:
                        return -1
                    if w[b] is None:
                        w[b] = False
                    elif w[b] is True:
                        return -1
            else:
                # set(a, si)
                if w[a] is None:
                    w[a] = si
                elif w[a] is not si:
                    return -1
        else:
            if has_b:
                # set(b, si)
                if w[b] is None:
                    w[b] = si
                elif w[b] is not si:
                    return -1
            else:
                if si:
                    # raise Conflict()
                    return -1
    for i in constraints:
        a = w[i-x]
        b = w[i+x]
        if a is True or b is True:
            pass
        else:
            if a is False and b is False:
                # raise Conflict()
                return -1
    return ''.join('0' if i is False else '1' for i in w)

def c_in():
    import sys
    # import os
    # try:
    #     file = open(os.path.join(sys.argv[0], r'../in-c-2.txt'))
    # except:
    file = sys.stdin
    n_test_case = int(file.readline())
    for i in range(n_test_case):
        s = file.readline().rstrip()
        x = int(file.readline())
...