Sparkling Stardust

Star is practicing a spell that makes stardust. To test her skill, she plans to use magic once a day for $N$ days and check how much stardust she can make.

Star has $K$ spells that make stardust. Call them spell 1, spell 2, ..., spell $K$. The number of stardust made by spell $i$ is

$\Delta Stardust = \lfloor base\_i(1+\frac{combo \cdot C}{100})(1+\frac{skill\_i \cdot s\_i}{100}) \rfloor$

• $\Delta Stardust$: the number of stardust made.
• $base\_i$: the number of stardust spell $i$ makes by default.
• $combo$: the number of consecutive days spells were used. For example, if Star used magic 5 days in a row before today, $combo = 5$.
• $skill\_i$: the skill level of spell $i$. For example, if Star used spell $i$ 3 times before today, $skill\_i = 3$.
• $C$ and $s\_i$ are constants.

Star's initial fatigue is 0. Each time spell $i$ is used, fatigue rises by $p\_i$. If fatigue exceeds 100, the wand breaks, no spell can be used afterward, and all stardust made so far is lost. Resting lowers fatigue by $R$, but resets the combo count to 0. Fatigue never drops below 0. If the reduction from resting is larger than the current fatigue, fatigue becomes 0.

Given Star's plan, compute the total number of stardust made over $N$ days.

The first line contains $N,K,C,R$ separated by spaces. ($1 \leq K \leq N \leq 100\,000$, $1 \leq C \leq 100$, $1 \leq R \leq 100$)

The second line contains $base\_1, \cdots , base\_K$ separated by spaces. ($1 \leq base\_i \leq 100\,000$)

The third line contains $s\_1, \cdots , s\_K$ separated by spaces. ($1 \leq s\_i \leq 100$)

The fourth line contains $p\_1, \cdots , p\_K$ separated by spaces. ($1 \leq p\_i \leq 100$)

From the fifth line, $N$ lines follow, each with one spell number $l\_i$ ($0 \leq l\_i \leq K$), the spell Star plans to use on day $i$. If $l\_i$ is 0, Star rests that day.

All numbers in the input are integers.

Print the total number of stardust made over $N$ days. If the wand breaks during the plan, print -1.