Kimchi

You ripen kimchi in a crock for $N$ days, from autumn into winter. You bury the kimchi on one day and take it out on that same day or on a later day.

A kimchi master states the conditions for good kimchi.

• The longer the aging time, the better the kimchi tastes.
• Kimchi freezes on cold days, so a higher temperature on the day you take it out makes the kimchi taste better.
• The value of the crock on the day you bury the kimchi affects the taste.

Written as a formula: if you bury the kimchi on day $i$ and take it out on day $j$ ($i \le j$), the aging time is $j - i$, and the aging time may be $0$. The taste is then

$(j - i) \times T_j + V_i$

where $T_j$ is the temperature on day $j$ and $V_i$ is the value of the crock on day $i$. Winter is coming, so the temperature only falls, and $T_i \ge T_{i+1}$ holds for every $i$.

Kimchi aged for too long is no good, so the aging time must be at most $D$.

Given the temperature and the value of the crock for every day, find the largest taste you can get.

The first line contains the number of days $N$ and the upper limit on the aging time $D$. ($1 \le D \le N \le 100000$)

The second line contains the temperatures $T_1, T_2, \dots, T_N$. Each $T_i$ is a natural number at most $10^9$, and $T_i \ge T_{i+1}$ holds for every $i$ with $1 \le i \le N-1$.

The third line contains the crock values $V_1, V_2, \dots, V_N$. Each $V_i$ is a natural number at most $10^9$.

Print the largest taste of the kimchi on one line.