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 j in range(0,t):
  s = input()
  x = int(input())
  w = ["-1"]*len(s)
  for i in range(0,len(s)):
    if s[i] == "0":
      if i+x< len(s):
        w[i+x] = "0"
      if i-x>=0 and w[i-x] != "1":
        w[i-x] = "0"
      elif i-x>=0:
        w = ["-1"]
        break
        
    else:
      if i-x>=0 and w[i-x] != "0":
        w[i-x] = "1"
      elif i+x<len(s) and w[i+x] !="0":
        w[i+x] = "1"
      else:
        w = ["-1"]
        break
  if len(w) != 1:
    for i in range(0,len(s)):
      if w[i] == "-1":
        w[i] = "1"
  print("".join(w))
