- Prepare
- Algorithms
- Greedy
- Accessory Collection

# Accessory Collection

# Accessory Collection

Victoria is splurging on expensive accessories at her favorite stores. Each store stocks types of accessories, where the accessory costs dollars (). Assume that an item's type identifier is the same as its cost, and the store has an unlimited supply of each accessory.

Victoria wants to purchase a total of accessories according to the following rule:

Any -element subset of the purchased items must contain

at leastdifferent types of accessories.

For example, if , , and , then she must choose accessories such that *any* subset of of the accessories will contain *at least* distinct types of items.

Given , , , and values for shopping trips, find and print the maximum amount of money that Victoria can spend during each trip; if it's not possible for Victoria to make a purchase during a certain trip, print `SAD`

instead. You must print your answer for each trip on a new line.

**Input Format**

The first line contains an integer, , denoting the number of shopping trips.

Each of the subsequent lines describes a single shopping trip as four space-separated integers corresponding to , , , and , respectively.

**Constraints**

- The sum of the 's for all shopping trips .

**Output Format**

For each shopping trip, print a single line containing either the maximum amount of money Victoria can spend; if there is no collection of items satisfying her shopping rule for the trip's , , , and values, print `SAD`

instead.

**Sample Input**

```
2
6 5 3 2
2 1 2 2
```

**Sample Output**

```
24
SAD
```

**Explanation**

*Shopping Trip 1:*

We know that:

- Victoria wants to buy accessories.
- The store stocks the following types of accessories: .
- For any grouping of of her accessories, there must be
*at least*distinct types of accessories.

Victoria can satisfy her shopping rule and spend the maximum amount of money by purchasing the following set of accessories: . The total cost is , so we print on a new line.

*Shopping Trip 2:*

We know that:

- Victoria wants to buy accessories.
- The store stocks type of accessory: .
- For any grouping of of her accessories, there must be
*at least*distinct types of accessories.

Because the store only carries type of accessory, Victoria cannot make a purchase satisfying the constraint that there be at least distinct types of accessories. Because Victoria will not purchase anything, we print that she is `SAD`

on a new line.