Ksonya and the Olympiad

The results of the Olympiad can be found after the event at the link oi.in.ua

Ksonya and her classmates arrived at the Olympiad $t$ minutes before it began. Due to quarantine restrictions, the organizers allow $m$ students to enter the auditorium every $w$ minutes.

This means that $m$ students will enter the Olympiad exactly $t$ minutes before it starts. Another $m$ students will enter $t-w$ minutes before the start, and another $m$ students will enter $t-2w$ minutes before the start, continuing in this pattern. Students can enter even at $0$ minutes before the start (i.e., when the Olympiad begins). However, no students can enter after the Olympiad has started.

There are $n$ students in the class, including Ksonya. How many students will be able to enter the auditorium before the Olympiad starts?

Input

The first line contains four integers $n,m,w,t$ ($1\le n,m,w,t\le 1,000$).

Output

Output a single number — the number of students who will manage to enter the Olympiad.

Examples

Note

Explanation for the first example:

• 4 minutes before the start, a group of two students enters the Olympiad.

• 3 minutes before, the remaining three students wait.

• 2 minutes before, the remaining three students wait.

• 1 minute before, another group of two students enters the Olympiad.

• At 0 minutes, one remaining student waits. Since time is up, only four students managed to enter.

Explanation for the second example:

• 4 minutes before the start of the Olympiad, a group of three students enters the Olympiad.

• 3 minutes before, the remaining three students wait.

• 2 minutes before, another group of three students can enter the Olympiad. Since there are no more students, all 6 students managed to enter.

Explanation for the third example:

• 6 minutes before the start of the Olympiad, a group of three students enters the Olympiad.

• 4 minutes before, the remaining seven students wait.

• 3 minutes before, another group of three students can enter the Olympiad.

• 1 minute before, the remaining four students wait.

• At 0 minutes, a group of three students enters the Olympiad.

• Time is up, so 9 students entered.