fairgame

Task

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.

Input data

The first line will contain the values of $N$, $K$, $M$, $P$, $Q$ in this order.

Output data

The first line will contain the value of the difference in dollars between Alice and Bob.

Constraints and clarifications

• $1 \leq N, K, M, P, Q \leq 5 \cdot 10^6$
• For $30$ points, $N \leq 4 \ 000$
• For $10$ more points, $N \leq 10 \ 000$, $K \leq 900$
• For $20$ more points, $N \leq 10 \ 000$

Example

stdin

6 3 5 4 2

stdout

2