Monster Game II

• Time limit: 1.00 s
• Memory limit: 512 MB

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. After killing a monster, you get a new skill factor (lower skill factor is better). 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

• $1 \le n \le 2 \cdot 10^5$
  
• $1 \le x \le 10^6$
  
• $1 \le s_i, f_i \le 10^6$
  

Example

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

Output:
2600

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