cheesecake is playing a mobile game where the goal is to spread a disease across the world. At any point in time, he may infect a healthy person with the pathogen, creating a *patient zero*. This pathogen spreads very quickly. Specifically, the number of infected people increases by a factor of each day, with the game starting on day .

cheesecake is trying to complete a very delicate mission in which he has to infect **exactly** people over a course of days. In other words, there must be **exactly** infected people on day . Help him find the minimum number of patient zeros he would have to create to complete his mission.

#### Constraints

For all subtasks, , ,

##### Subtask 1 [20%]

##### Subtask 2 [20%]

##### Subtask 3 [60%]

No additional constraints.

#### Input Specification

The only line of input will have , , and , separated by spaces.

#### Output Specification

Output the required answer, the minimum number of patient zeros cheesecake would have to create.

#### Sample Input 1

`8 2 1`

#### Sample Output 1

`4`

#### Sample Input 2

`9 3 2`

#### Sample Output 2

`1`

#### Sample Input 3

`10 7 10`

#### Sample Output 3

`4`

#### Explanation for Sample Outputs

In the first case, the optimal solution is to infect people on day .

In the second case, cheesecake should infect just one person on day . On day there will be people infected. And on day there will be , as required.

In the third case, cheesecake should wait until day , infect one person, then infect more on day .

## Comments