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
t = int(input())

from collections import defaultdict


class FailUpdate(Exception):
    pass


def must_have_value(w, idx, val):
    if w[idx] != "" and w[idx] != val:
        raise FailUpdate()
    w[idx] = val

def solve():
    s = input()
    n = len(s)
    x = int(input())
    w = [""] * n
    
    deps = defaultdict(list)
    for i in range(0, n):
        left = i-x
        right = i+x
        if left >= 0:
            deps[i].append(left)
        if right <= n-1:
            deps[i].append(right)

    try:
        for i in range(n):
            if len(deps[i]) == 0 and s[i] == "1":
                return -1
        for i in range(n):
            if len(deps[i]) == 1:
                must_have_value(w, deps[i][0], s[i])

        for i in range(n):
            if len(deps[i]) == 2 and s[i] == "0":
                dep1, dep2 = deps[i]
                must_have_value(w, dep1, "0")
                must_have_value(w, dep2, "0")
    except FailUpdate:
        return "-1"

    for i in range(n):
        if len(deps[i]) == 2 and s[i] == "1":
            dep1, dep2 = deps[i]
            if w[dep1] == "0" and w[dep2] == "0":
                return "-1"

    for i in range(n):
        if w[i] == "":
            w[i] = "1"
    return "".join(w)
        

for __ in range(t):
    print(solve())
