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D. Professional layer

time limit per test

3 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputCardbluff 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

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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