Winnie is playing the latest hot mobile game, AliensXBattle 2. In this game, Winnie has aliens on the field. Each alien starts at level , but can be upgraded by using coins and alien drinks. The maximum level of each alien is . Each alien has a power level. The power level of each alien changes based on level. Help Winnie determine the maximum sum of power levels she can achieve.

#### Input Specification

The first line of input contains two integers and . is the amount of coins Winnie has, and is the amount of alien drinks Winnie has.

The second line of input contains two integers and . is the amount of coins to level up a alien, and is the amount of energy drinks needed to level up a alien.

Each of the next lines of input will contain integers, . represents the power level of the alien at level . It is **not** guaranteed that a alien will have a power level increases as they level up.

#### Output Specification

Output the maximum power level Winnie can achieve by upgrading her aliens.

#### Constraints

(Hint: What does these constraints tell you about the problem?)

#### Sample Input 1

```
1 1
1 1
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
```

#### Sample Output 1

`7`

## Comments

I feel like there is something stupidly obvious that I'm missing, so I'm leaving this comment here for whenever I finally figure out what I'm doing wrong and come back to reconsider my choices in life