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

I = lambda: int(input())
RL = readline = lambda: sys.stdin.readline().strip('\n')
RM = readmap  = lambda x = int: map(x,readline().split(' '))

#C
for _ in range(I()):
    s,x = RL(),I();n = len(s)
    w = ['1']*n
    for ind,i in enumerate(s):
        if i == '0':
            i1,i2 = ind-x,ind+x
            if i1 >=0: w[i1] = '0'
            if i2 < n: w[i2] = '0'

    imp = False 
    for ind,i in enumerate(s):
        i1,i2 = ind-x,ind+x
        flag = (i1 >=0 and w[i1] == '1') or (i2 < n and w[i2] == '1')
        if "01"[flag] != i: imp = True; break
    print(''.join(w) if not imp else -1)
