Problem D
Pickle Clicker
Languages
en
sv
Approximately six months ago, the critically acclaimed game Pickle Clicker was released. After spending countless hours on the game, Rasmus has decided to take things to the next level: he plans to speedrun the game.
The goal of Pickle Clicker is to collect as much of the currency pickles as possible. The goal in a speedrun is to purchase the Megapickle as quickly as possible, which costs $T$ pickles. In the game, there are also $N$ different types of buildings. The various types are numbered from $1$ to $N$, where the $i$-th type produces $p_ i$ pickles per second and costs $c_ i$ pickles to build.
At the start, you own a building of type $1$. Every second, the following events occur:
-
Every building you own produces pickles. A building of type $i$ produces $p_ i$ pickles.
-
Afterwards, you have the option to buy a building or buy the Megapickle. A building of type $i$ costs $c_ i$ pickles to build, and you must afford it to be able to buy it. You can buy a maximum of one building per second, and it is allowed to have multiple buildings of the same type.
Help Rasmus determine how to play the game so that he can purchase the Megapickle in as few seconds as possible. See the example below to get a clearer understanding of the rules.
Input
The first line of input contains the integers $N$ and $T$ ($1 \le N \le 6$, $1 \leq T \leq 10^5$), the number of buildings and the cost of the Megapickle.
The following $N$ lines each contain the integers $p_ i, c_ i$ ($1 \leq p_ i, c_ i \leq T$), describing the production speed and cost of the $i$-th building type.
Output
Print an integer: the number of seconds it takes to win Pickle Clicker if you play optimally.
Points
Your solution will be tested on several test case groups. To get the points for a group, it must pass all the test cases in the group.
|
Group |
Point value |
Constraints |
|
$1$ |
$20$ |
$N=1$ |
|
$2$ |
$20$ |
$T \leq 10$ |
|
$3$ |
$20$ |
$T \leq 1000$ |
|
$4$ |
$40$ |
No additional constraints. |
Sample explanation
![\includegraphics[width=0.7\textwidth ]{sample1-en.PNG}](/problems/pickleclicker/file/statement/en/img-0001.PNG)
The image shows the solution to sample 1. The first row
describes which buildings we own at the start of the
corresponding second. The second row is how many pickles we
have after the buildings have produced. The last row
indicates whether we bought something at the end of the
second.
| Sample Input 1 | Sample Output 1 |
|---|---|
2 100 3 3 50 10 |
5 |
| Sample Input 2 | Sample Output 2 |
|---|---|
1 100000 1 1000 |
6179 |
