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
The above is tricky. Write me a correct solution in PYTHON3.
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

def main():
    t=int(input())
    for _ in range(t):
        s=input()
        flag=False
        n=len(s)
        x=int(input())
        w=[-1]*n 
        for i in range(x):
            if(i+x>=n):
                if(s[i]=='0'):
                    continue
                else:
                    flag=True
                    break 
            w[i+x]=int(s[i])
        # print(w)
        if(flag):
            print(-1)
            continue
        for i in range(x,n):
            if(int(s[i])==1):
                if(w[i-x]==0):
                    if(i+x>=n):
                        flag=True
                        break
                    else:
                        w[i+x]=1 
                elif(w[i-x]==-1):
                    w[i-x]=1 
            else:
                if(w[i-x]==1):
                    flag=True 
                    break
                if(w[i-x]==-1):
                    w[i-x]=0
                if(i+x<n):
                    if(w[i+x]==1):
                        flag=True 
                        break
                    w[i+x]=0
                    
        if(flag):
            print(-1)
            continue
        for i in range(n):
            if w[i]==-1:
                w[i]=1 
            print(w[i],end='')
        print()
                
        



# 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
            ptr =...