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
for _ in range(int(input())):
    w = input()
    x = int(input())
    m = len(w)
    f = 0
    s = set()
    l = ["1"] * m
    for i in range(len(w)):
        if w[i] == "0":
            if i+x < m and i+x > -1:
                s.add(i + x)

            if i-x > -1 and i-x < m:
                s.add(i-x)

    for i in range(len(w)):
        if w[i] == "1":
            if (i-x in s and i+x in s) or (i+x >= m and i-x < 0) or (i-x in s and i+x >= m) or (i+x in s and i-x < 0):
                f = 1
                break

    if f == 1:
        print(-1)
        continue

    for i in s:
        l[i] = "0"

    print("".join(l))