1. Car Wash
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Max arrived at a self-service car wash to wash his car. He can choose one of three available payment rates.

  1. Fixed amount — pay $$$X$$$ rubles for the entire wash regardless of the time and water used;
  2. Pay-per-minute — pay $$$Y$$$ rubles for each minute spent washing;
  3. Pay-per-liter — pay $$$Z$$$ rubles for each liter of water used during the wash.

Max knows that he will completely wash the car in $$$T$$$ minutes, using $$$V$$$ liters of water in the process.

Help Max determine the minimum amount of rubles needed to pay for the car wash if he chooses the rate optimally.

Input

The first line contains an integer $$$X$$$ ($$$1 \le X \le 10^4$$$) — the fixed payment rate for the car wash.

The second line contains an integer $$$Y$$$ ($$$1 \le Y \le 10^4$$$) — the cost per minute of washing.

The third line contains an integer $$$Z$$$ ($$$1 \le Z \le 10^4$$$) — the cost per liter of water.

The fourth line contains an integer $$$T$$$ ($$$1 \le T \le 10^4$$$) — the number of minutes required to wash the car.

The fifth line contains an integer $$$V$$$ ($$$1 \le V \le 10^4$$$) — the volume of water in liters required to wash the car.

Output

Output a single integer — the minimum amount of rubles to pay for the car wash.

Scoring

Solutions that work correctly for $$$T = 1$$$, $$$V = 1$$$ will be scored with $$$20$$$ points.

Examples
Input
1
1
1
1
1
Output
1
Input
200
10
18
14
15
Output
140
Note

In the first example, the total costs for all rates are the same and equal to $$$1$$$.

In the second example, the most advantageous option is to pay by the second rate, paying for $$$14$$$ liters of water at $$$10$$$ rubles per liter.