# Fill The Truck

A Warehouse manager needs to create a shipment to fill a truck. All the products in the warehouse are in boxes of the same size. Each product is packed in some number of units per box.

Given the number of boxes, the truck can hold, write an algorithm to determine the maximum number of units of any mix of products that can be shipped.

### Input

The input consists of five arguments:

`num`

: an `integer`

representing the number of products

`boxes`

: a `list of integers`

representing the number of available boxes for products

`unitSize`

: an `integer`

representing size of `unitsPerBox`

`unitsPerBox`

: a `list of integers`

representing the number of units packed in each box

`truckSize`

: an `integer`

representing the number of boxes the truck can carry.

### Output

Return an `integer`

representing the maximum units that can be carried by truck.

### Constraints

`1 <= |boxes| <= 10^5`

`|boxes| == |unitsPerBox|`

`1 <= boxes[i] <= 10^7`

`1 <= i <= |boxes|`

`1 <= unitsParBox[i] <= 10^5`

`1 <= j <= |unitsPerBox|`

`1 <= truckSize <= 10 ^ 8`

### Examples

#### Example 1:

##### Input:

num = `3`

boxes = `[1, 2, 3]`

unitSize = `3`

unitsPerBox = `[3, 2, 1]`

truckSize = `3`

##### Output: `7`

##### Explanation:

`Product 0:`

because `boxes[0] = 1`

, we know there is `1`

box in product `0`

. And because `unitsPerBox[0] = 3`

, we know there is `1`

box with `3`

units in product `0`

.

`Product 1:`

`2`

boxes with `2`

units each

`Product 2:`

`3`

boxes with `1`

unit each

Finally, we have packed products like a list: `[3, 2, 2, 1, 1, 1]`

The `truckSize`

is `3`

, so we pick the top `3`

from the above list, which is `[3, 2, 2]`

, and return the sum `7`

.

The maximum number of units that can be shipped = `3 + 2 + 2 = 7`

units