Pull-ups

Limits: 2 sec., 512 MiB

This statement was translated automatically from Ukrainian.

Today was a really difficult day for Zenik. He failed to solve the "A + B" problem on Algotester and to top it all off, it is raining heavily. Probably the only thing left for him to do was to go do some pull-ups. However, Zenik, as a true athlete, set goals for himself that need to be met.

For example, this time he needs to complete \(n\) sets, such that the number of pull-ups in each set is not less than \(k\). In addition, the total number of pull-ups for the workout cannot be less than \(m\). Output the minimum total number of pull-ups Zenik needs to do to fulfill today’s goal if Zenik distributes the number of pull-ups optimally.

Input

The single line contains three integers \(n, m, k\) — the number of sets, the minimum total number of pull-ups for the workout, and the minimum number of pull-ups per set, respectively.

Output

Output a single number — the minimum number of pull-ups.

Constraints

\(1 \le n, m, k \le 10^9\),

\(n \cdot k \le 10^9\).

Scoring consists of the following blocks:

• 1 point for each example from the statement,

• 20 points: \(n = 1\),

• 30 points: \(n \cdot k \le m\),

• 48 points: no additional constraints.

You will receive the points for a block only if your program passes all tests in that block.

Samples

Input (stdin) сopy	Output (stdout) сopy
2 5 3	6

Input (stdin) сopy	Output (stdout) сopy
2 7 3	7

Notes

In the first example, the optimal distribution of pull-ups would be to do three pull-ups in each of the two sets to satisfy the conditions.

In the second example, one of the optimal distributions of pull-ups would be to do four pull-ups in the first set and three in the second.