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())
for _ in range(t):
    s = str(input())
    x = int(input())
    n = len(s)
    w = [-1]*n
    for i in range(n):
        j = i-x
        k = i+x
        if 0 <= j < n and 0 <= k < n:
            if s[i] == '0':
                w[j] = '0'
                w[k] = '0'
        elif  0 <= j < n:
            if s[i] == '1':
                w[j] = '1'
            else:
                w[j] = '0'
        elif  0 <= k < n:
            if s[i] == '1':
                w[k] = '1'
            else:
                w[k] = '0'
    for i in range(n):
        if w[i] == -1:
            w[i] = '1'
    t = [-1]*n
    for i in range(n):
        j = i-x
        k = i+x
        if 0 <= j < n and 0 <= k < n:
            if w[j] == '1':
                t[i] = '1'
            elif w[k] == '1':
                t[i] = '1'
            else:
                t[i] = '0'
        elif 0 <= j < n:
            if w[j] == '1':
                t[i] = '1'
            else:
                t[i] = '0'
        elif 0 <= k < n:
            if w[k] == '1':
                t[i] = '1'
            else:
                t[i] = '0'
        else:
            t[i] = '0'
    t = ''.join(t)
    if s == t:
        print(''.join(w))
    else:
        print(-1)
