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
import sys
sys.setrecursionlimit(2147483647)

def solve(s,x):
  l = len(s)
  ans = [1]*l
  flags = [0]*l
  point = 0
  searched = -1
  for point in range(l):
    a = s[point]
    if a == '0':
      if(point - x >= 0):
        if(flags[point - x]):
          if(ans[point - x] != 0):
            return -1
        else:
          ans[point - x] = 0
          flags[point - x] = 1
      if(point + x < l):
        # if(flags[point + x]):
        #   if(ans[point + x] != 0):
        #     return -1
        # else:
        ans[point + x] = 0
        flags[point + x] = 1
    else:
      if(point - x < 0):
        if(point + x >= l):
          return -1
        else:
          # if(point + 2*x >= l):
          ans[point + x] = 1
          flags[point + x] = 1
          # elif(s[point + 2*x] == '0'):
          #   return -1
          # else:
          #   ans[point + x] = 1
          #   flags[point + x] = 1
      else:
        if(point - 2*x < 0):
          ans[point - x] = 1
          flags[point - x] = 1
        else:
          if flags[point - x] and ans[point - x] == 0:
            if(point + x >= l):
              return -1
            else:
              # if(point + 2*x >= l):
              ans[point + x] = 1
              flags[point + x] = 1
              # elif(s[point + 2*x] == '0'):
              #   return -1
              # else:
              #   ans[point + x] = 1
              #   flags[point + x] = 1
          else:
            ans[point - x] = 1
            flags[point - x] = 1
  return ''.join(list(map(str, ans)))



def main():
  t = int(input())
  ans = []
  for _ in range(t):
    s = input()
    x = int(input())
    ans.append(solve(s,x))
  for r in ans:
    print(r)
  

if __name__=='__main__':
  main()