# 2020 USACO January Silver

# Loan Repayment

Farmer John owes Bessie **n** gallons of milk. He has to give her the milk within **k** days. However, he doesn't want to give the milk away too quickly. On the other hand, he has to make forward progress on the loan, so he must give Bessie at least **m** gallons of milk each day.

Here is how Farmer John decides to pay back Bessie. He first picks a positive integer **x**. He then repeats the following procedure every day:

- Assuming that Farmer John has already given Bessie
**g**gallons, compute (**n**−**g**) /**x**rounded down. Call this number**y**. - If
**y**is less than**m**, set**y**to**m**. - Give Bessie
**y**gallons of milk.

Determine the largest **x** such that if Farmer John follows the above procedure, Farmer John gives Bessie at least **n** gallons of milk after **k** days.

#### Input

Three positive integers **n** (**1** ≤ **n** ≤ `10`

), ^{12}**k** (**1** ≤ **k** ≤ `10`

), ^{12}**m** (**1** ≤ **m** ≤ `10`

), satisfying ^{12}**k** * **m** < **n**.

#### Output

Output the largest positive integer **x** such that Farmer John will give Bessie at least **n** gallons using the above procedure.

#### Example

For the first test case, when **x** = **2** Farmer John gives Bessie **5** gallons on the first day and **m** = **3** gallons on each of the next two days.

10 3 3

2