Fişierul intrare/ieşire: fairgame.in, fairgame.out Sursă IIOT 2019-20 Runda 3 Autor Alexandru Petrescu Adăugată de Timp execuţie pe test 0.4 sec Limită de memorie 256000 kbytes Scorul tău N/A Dificultate N/A

# Fairgame

Alice and Bob are playing a game. They have a pile of N rocks. Alice makes the first move, then Bob does the second, and so on... In each turn, the player that has to move takes at least 1 rock and maximum K rocks. If one takes an odd number of rocks, then they have to pay M dollars. When the pile is empty, the player who made the last move gets P dollars and the other one gets Q dollars. After the game ends, Alice will end up with an amount of dollars, let's call it X, and Bob will end up with another amount of dollars, let's call it Y. Knowing that they play optimally, which means Alice wants to maximize the number X - Y Bob wants to minimize this number, then find out X - Y after the game ends.

## Date de intrare

On the first line of input in the file fairgame.in there are the values of N, K, M, P, Q in this order.

## Date de ieşire

On the first line of the output file fairgame.out the value of the difference in dollars between Alice and Bob should be written

## Restricţii

• 1 ≤ N, K, M, P, Q ≤ 5 * 10^6
• Pentru 30 puncte, \$N ≤ 4000
• Pentru alte 10 puncte, N ≤ 10000, K ≤ 900
• Pentru alte 20 puncte, N ≤ 10000

## Exemplu

fairgame.infairgame.out
6 3 5 4 2
2

### Explicaţie

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