Insect Reproduction

Problem Background

Special for beginners, ^_^

Problem Description

Scientists discovered a special kind of insect in a tropical forest; this insect reproduces very strongly. Every pair of eggs takes two months to grow into adults. After becoming adults, they need $x$ months before they can reproduce, and then they lay $y$ pairs of eggs each month. Assume no adult ever dies; in the first month there is only one pair of adults, and the first month after eggs grow into adults they do not lay eggs (they start laying after $x$ months). After $Z$ months, how many pairs of adults are there in total? $1 \le X \le 20$, $1 \le Y \le 20$, $X \le Z \le 50$.

Input Format

The values $x, y, z$.

Output Format

The number of pairs of adults after $Z$ months.

Sample Input 1

1 2 8

Sample Output 1

37

Constraints

1s, 1024KiB for each test case.