# Number systems

# Number systems

*Chuck Norris counted to infinity. Twice.*

*(Internet-folklore)*

The young mathematician Vovochka is not lazy, so he wrote out all positive integers in ascending order. In a fit of diligence he translated all the numbers of the series into the number system with the base **b**. Then Vovochka struck out all the numbers of the series, which are a record of some number in the number system with the base **c**.

Vovochka's diligence was over, and he asked you, as his programmer friend, to find the **n**-th non-crossed number of the series. Help the young mathematician Vovochka!

#### Input

Three numbers **n**, **b** and **c** (**1** ≤ **n** ≤ `10`

, ^{7}**2** < **c** < **b** ≤ **6**). In number systems with bases larger than **10** as digits except **0**, ..., **9** the lowercase letters of the Latin alphabet **a**, ..., **z** are used.

#### Output

Print (in decimal system) the **n**-th non-crossed number of the series.

2 3 2

5

1 3 2

2