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
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()
    try:
        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)
                else:
                    set(a, si)
            else:
                if has_b:
                    set(b, si)
                else:
                    if si:
                        raise Conflict()
        for i in constraints:
            a = w[i-x]
            b = w[i+x]
            if a or b:
                pass
            else:
                if a is False and b is False:
                    raise Conflict()
    except Conflict:
        return -1
    return ''.join('0' if i is False else '1' for i in w)

def c_in():
    import sys, 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())
        print(controller(s,x))

if __name__ == '__main__':
    c_in()

