# Luck Balance

# Luck Balance

Lena is preparing for an important coding competition that is preceded by a number of sequential preliminary contests. Initially, her luck balance is 0. She believes in "saving luck", and wants to check her theory. Each contest is described by two integers, and :

- is the amount of luck associated with a contest. If Lena
*wins*the contest, her luck balance will*decrease*by ; if she*loses*it, her luck balance will*increase*by . - denotes the contest's
*importance rating*. It's equal to if the contest is*important*, and it's equal to if it's*unimportant*.

If Lena loses no more than *important* contests, what is the maximum amount of luck she can have after competing in all the preliminary contests? This value *may* be negative.

**Example**

```
Contest L[i] T[i]
1 5 1
2 1 1
3 4 0
```

If Lena loses all of the contests, her will be . Since she is allowed to lose important contests, and there are only important contests, she can lose all three contests to maximize her luck at .

If , she has to win at least of the important contests. She would choose to win the lowest value important contest worth . Her final luck will be .

**Function Description**

Complete the *luckBalance* function in the editor below.

luckBalance has the following parameter(s):

*int k*: the number of important contests Lena can lose*int contests[n][2]:*a 2D array of integers where each contains two integers that represent the luck balance and importance of the contest

**Returns**

*int:*the maximum luck balance achievable

**Input Format**

The first line contains two space-separated integers and , the number of preliminary contests and the maximum number of important contests Lena can lose.

Each of the next lines contains two space-separated integers, and , the contest's luck balance and its importance rating.

**Constraints**

**Sample Input**

```
STDIN Function
----- --------
6 3 n = 6, k = 3
5 1 contests = [[5, 1], [2, 1], [1, 1], [8, 1], [10, 0], [5, 0]]
2 1
1 1
8 1
10 0
5 0
```

**Sample Output**

```
29
```

**Explanation**

There are contests. Of these contests, are important and she cannot lose more than of them. Lena maximizes her luck if she wins the important contest (where ) and loses all of the other five contests for a total luck balance of .