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
from sys import stdin
###############################################################
def iinput(): return int(stdin.readline())
def minput(): return map(int, stdin.readline().split())
def linput(): return list(map(int, stdin.readline().split()))
###############################################################

def f(s, x):
     w = [None for _ in range(len(s))]
     for i in range(len(s)):
          if s[i] == '1':
               if i-x<0 and i+x>=len(s):
                    return -1
               try:
                    if w[i-x] == '0' and w[i+x] == '0':
                         return -1
               except: pass

               if i - x >= 0:
                    if w[i-x] == '0':
                         if i+x < len(s) and w[i+x] != '0':
                              w[i+x] = '1'
                         else: return -1
                    elif w[i-x] == None:
                         w[i-x] = '1'
                         if len(s) > i+x >= len(s)-x:
                              w[i+x] = '1'

               elif i + x < len(s):
                    if w[i+x] == '0':
                         return -1
                    elif w[i+x] == None:
                         w[i+x] = '1'

          else:
               if i - x >= 0:
                    if w[i-x] =='1':
                         return -1
                    w[i-x] = '0'
               if i + x < len(s):
                    if w[i+x] == '1':
                         return -1
                    w[i+x] = '0'

     for i in range(len(w)):
          if w[i] == None: w[i] = '0'

     return ''.join(w)


t = iinput()
while t:
     t-=1
     s = input()
     x = iinput()
     print(f(s, x))


