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D. Professional layer
time limit per test
3 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

Cardbluff is popular sport game in Telegram. Each Cardbluff player has ever dreamed about entrance in the professional layer. There are $$$n$$$ judges now in the layer and you are trying to pass the entrance exam. You have a number $$$k$$$ — your skill in Cardbluff.

Each judge has a number $$$a_i$$$ — an indicator of uncertainty about your entrance to the professional layer and a number $$$e_i$$$ — an experience playing Cardbluff. To pass the exam you need to convince all judges by playing with them. You can play only one game with each judge. As a result of a particular game, you can divide the uncertainty of $$$i$$$-th judge by any natural divisor of $$$a_i$$$ which is at most $$$k$$$. If GCD of all indicators is equal to $$$1$$$, you will enter to the professional layer and become a judge.

Also, you want to minimize the total amount of spent time. So, if you play with $$$x$$$ judges with total experience $$$y$$$ you will spend $$$x \cdot y$$$ seconds.

Print minimal time to enter to the professional layer or $$$-1$$$ if it's impossible.

Input

There are two numbers in the first line $$$n$$$ and $$$k$$$ ($$$1 \leq n \leq 10^6$$$, $$$1 \leq k \leq 10^{12}$$$) — the number of judges and your skill in Cardbluff.

The second line contains $$$n$$$ integers, where $$$i$$$-th number $$$a_i$$$ ($$$1 \leq a_i \leq 10^{12}$$$) — the uncertainty of $$$i$$$-th judge

The third line contains $$$n$$$ integers in the same format ($$$1 \leq e_i \leq 10^9$$$), $$$e_i$$$ — the experience of $$$i$$$-th judge.

Output

Print the single integer — minimal number of seconds to pass exam, or $$$-1$$$ if it's impossible

Examples
Input
3 6
30 30 30
100 4 5
Output
18
Input
1 1000000
1
100
Output
0
Input
3 5
7 7 7
1 1 1
Output
-1