Problem B
Bíókort

Arnar’s last cinema card.

Many years ago the Bíótríó was founded. The original members were Arnar, Hannes and Sara. The goal of the group was simple: Go to the cinema frequently and cheaply. They managed to go upwards of a hundred times per year, sometimes even more often. A few years after the founding Halldór was added to the group, making it The Movie Quartet instead.

But how did they manage to go to the cinema so often without going broke? The answer is the cinema card! Smárabíó once offered a year long card that you paid for once and could then use on each movie exactly once. The card was not bound to a specific individual, you could share a cinema card between many people. By buying cinema cards when they were on sale, the group managed to pay only $240$ ISK for each ticket on average one year. Unfortunately this offer no longer exists.

The Movie Quartet did not like skipping out on movies, but sometimes they brought others with them. Each year they looked into what people they could bring with them to the movies. They even knew exactly how popular each movie would be, that is to say, how many group members would be going to each movie.

How did they minimise the cost of the tickets over the year?

Input

The first line of input contains three integers $n$, the number of movies in cinemas this year, $m$, the price of a single use ticket and $k$, the price of a cinema card for the entire year, both given in ISK. Finally there are $n$ lines each describing a single movie. Each movie is given as its name and its popularity, separated by a space.

Each movie’s name is unique and is at least $1$ and at most $20$ English letters or digits. It is always guaranteed that $0 \leq m \leq 100\, 000$ and $0 \leq k \leq 10\, 000\, 000$. Each popularity is at least $0$ and at most $10^6$.

Output

Print the number of cinema cards they should buy and the total cost of seeing all the movies over the course of the year if they choose the number of cards optimally, to minimise cost, in ISK. If there are many correct answers you may print any one of them. Note that there are only $10^6$ cinema cards minted each year, so that’s the maximum amount that can be purchased.

Scoring

12 2250 24000
Oppenheimer 5
GranTurismo 4
BlueBeetle 4
Expend4bles 4
SawX 2
TheMarvels 4
BalladOfSongbirds 4
GodzillaMinusOne 6
AquamanLostKingdom 2
Argylle 3
TheBeekeeper 4
DunePart2 4

2 97500

5 1 2
Omurleg 0
Leleg 1
Ok 2
God 3
Frabaer 4

2 7