You are playing a game that consists of $n$ levels. Each level has a monster. On levels $1,2,\dots,n-1$, you can either kill or escape the monster. However, on level $n$ you must kill the final monster to win the game.

Killing a monster takes $sf$ time where $s$ is the monster's strength and $f$ is your skill factor (lower skill factor is better). After killing a monster, you get a new skill factor. What is the minimum total time in which you can win the game?

Input

The first input line has two integers $n$ and $x$: the number of levels and your initial skill factor.

The second line has $n$ integers $s_1,s_2,\dots,s_n$: each monster's strength.

The third line has $n$ integers $f_1,f_2,\dots,f_n$: your new skill factor after killing a monster.

Output

Print one integer: the minimum total time to win the game.

Constraints

• $1 \le n \le 2 \cdot 10^5$
• $1 \le x \le 10^6$
• $1 \le s_1 \le s_2 \le \dots \le s_n \le 10^6$
• $x \ge f_1 \ge f_2 \ge \dots \ge f_n \ge 1$

Example

Input:

5 100
20 30 30 50 90
90 60 20 20 10

Output:

4800

Explanation: The best way to play is to kill the third and fifth monster.