A. As Fast As Possible
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Monocarp plays a new computer game. Each level of this game can be represented as the coordinate axis $$$oX$$$.

To beat the current level, Monocarp's character has to travel from the point $$$0$$$ to the point $$$n$$$. There are two ways to move in the game:

  • walk to an adjacent point; it takes $$$a$$$ seconds (i. e. move from $$$x$$$ to $$$x - 1$$$ or $$$x + 1$$$ in $$$a$$$ seconds);
  • jump to a point with distance $$$d$$$ from the current one; the leap takes $$$b$$$ seconds (i. e. move from $$$x$$$ to $$$x - d$$$ or $$$x + d$$$ in $$$b$$$ seconds).

Note that it's possible that Monocarp's character will travel through some points that are to the left of point $$$0$$$ or to the right of point $$$n$$$; it's not against the rules, since the level is infinite.

You have to calculate the minimum time required to reach the point $$$n$$$ from the point $$$0$$$.

Input

The first line contains four integers $$$n$$$, $$$a$$$, $$$b$$$ and $$$d$$$ ($$$1 \le n \le 1\,000$$$, $$$1 \le a \le 1\,000$$$, $$$1 \le b \le 1\,000$$$, $$$1 \le d \le n$$$) — the point Monocarp's character has to reach, the time required to walk to an adjacent point, the time required to leap, and the length of the leap.

Output

Print one integer — the minimum time required to reach the point $$$n$$$ from the point $$$0$$$.

Examples
Input
9 7 6 5
Output
19
Input
20 5 10 15
Output
35
Input
4 3 5 2
Output
10
Note

In the first example, it's possible to walk to the left for $$$7$$$ seconds. Then Monocarp's character ends up in the point $$$-1$$$. Then he can leap to the right twice, the first leap ends in the point $$$4$$$, and the second leap ends in the point $$$9$$$. Two leaps take $$$12$$$ seconds. So, Monocarp reaches the goal in $$$7 + 12 = 19$$$ seconds.

In the second example, it's possible to start by leaping to the right. Then the character ends up in the point $$$15$$$, spending $$$10$$$ seconds. Then he has to walk to the right $$$5$$$ times, so he reaches the point $$$20$$$. The total time spent by Monocarp will be equal to $$$10 + 5 \cdot 5 = 35$$$ seconds.

In the third example, it's possible to leap to the right twice. Then the character ends up in the point $$$4$$$, spending $$$10$$$ seconds.