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
# Author: S Mahesh Raju
# Username: maheshraju2020
# Date: 25/08/2020

from sys import stdin, stdout, setrecursionlimit
from math import gcd, ceil, sqrt
from collections import Counter, deque
from bisect import bisect_left, bisect_right
ii1 = lambda: int(stdin.readline().strip())
is1 = lambda: stdin.readline().strip()
iia = lambda: list(map(int, stdin.readline().strip().split()))
isa = lambda: stdin.readline().strip().split()
setrecursionlimit(100000)
mod = 1000000007

def check(a, b, x):
    cur = []
    for i in range(len(a)):
        if i >= x and a[i - x] == '1':
            cur.append('1')
        elif i + x < len(a) and a[i + x] == '1':
            cur.append('1')
        else:
            cur.append('0')
    cur = "".join(cur)
    if cur == b:
        return True
    return False
        

tc = ii1()
for _ in range(tc):
    s = is1()
    x = ii1()
    res = ['1'] * len(s)
    for i in range(len(s)):
        if s[i] == '0':
            if i >= x:
                res[i - x] = '0'
            if i + x < len(s):
                res[i + x] = '0'
    if check(res, s, x):
        print("".join(res))
    else:
        print(-1)