human
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
Solve the task in PYTHON.

=====
What is a Python program to print the answer on a separate line as follows:?
assistant
#Here is Python program to print the answer on a separate line as follows:
.

from __future__ import division, print_function
import os
import sys
from io import BytesIO, IOBase
if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from future_builtins import ascii, filter, hex, map, oct, zip
# ------------------------------ TEMPLATE ABOVE THIS --------------------------------

def verify(w,s,x):
    n=len(w)
    for i in range(n):
        if i-x>=0 and w[i-x]=="1":
            if s[i]=="1":
                continue
            else:
                return False
        elif i+x<n and w[i+x]=="1":
            if s[i]=="1":
                continue
            else:
                return False
        else:
            if s[i]=="0":
                continue
            else:
                return False
    return True
    # if the character wi−x exists and is equal to 1, then si is 1 (formally, if i>x and wi−x= 1, then si= 1);
    # if the character wi+x exists and is equal to 1, then si is 1 (formally, if i+x≤n and wi+x= 1, then si= 1);
    # if both of the aforementioned conditions are false, then si is 0.


def solve():
    s=input()
    x=int(input())
    n=len(s)
    A=["1"]*n
    for i in range(n):
        if s[i]=="0":
            if i-x>=0:
                A[i-x]="0"
            if i+x<n:
                A[i+x]="0"
    w="".join(A)
    if verify(w,s,x):
        print(w)
    else: 
        print(-1)
    

def main():
    t=int(input())
    # print(t)
    for _ in range(t):
        solve()
    

    return

# ------------------------------ TEMPLATE BELOW THIS --------------------------------
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
           ...