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, stdout
input = stdin.readline
#print = stdout.write

for _ in range(int(input())):
    s = input().strip()
    x = int(input())
    w = ['1']*len(s)
    for idx, ch in enumerate(s):
        if ch=='0':
            if idx-x>=0:
                w[idx-x] = '0'
            if idx+x<=len(s)-1:
                w[idx+x] = '0'
    w = ''.join(w)
    for idx, ch in enumerate(s):
        if ch == '1':
            if idx-x<0 and idx+x>len(s)-1:
                print(-1)
                break
            if idx-x>=0 and idx+x>len(s)-1 and w[idx-x]!='1':
                print(-1)
                break
            if idx+x<len(s) and idx-x<0 and w[idx+x]!='1':
                print(-1)
                break
            if (idx+x<len(s) and w[idx+x]!='1') and (idx-x>=0 and w[idx-x]!='1'):
                print(-1)
                break
    else:
        print(w)