**NOTE: The test data for this problem are stronger than the contest version. Solutions that AC there may not
get AC here.**

Pusheen is playing Neko Atsume! She has a lot of toys and has laid them out to maximize her fish income. She wants to know how efficient her layout will be though.

After doing a lot of critical thinking and real-time programming, Pusheen has boiled down the fish income in terms
of a single variable - the *beauty* of the arrangement of toys. She thus defines to be the fish income given
that her layout has beauty . After some more computation, Pusheen has realized that for all , . Otherwise, .

Pusheen has layouts, layout having beauty . Compute for many values of .

#### Constraints

#### Input Specification

The first line contains five space-separated integers, , , , , and .

The next lines each contain a single positive integer, .

#### Output Specification

Output lines, the values in order.

#### Sample Input

```
2 0 2 0 3
1
2
3
```

#### Sample Output

```
2
4
4
```

## Comments