Description

Scientists have discovered a special insect in the tropical forest with strong reproductive ability. Each pair of adult insects lays $y$ pairs of eggs every $x$ months, and each pair of eggs takes two months to mature into adults. Assume that no adult dies, there is only one pair of adults in the first month, and newly matured adults do not lay eggs in their first month (they lay eggs after $x$ months). How many pairs of adults are there after $z$ months? $1\leq x\leq 20$, $1\leq y\leq 20$, $x < z \leq 50$.

Input Format

Values of $x$, $y$, and $z$.

Output Format

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

Sample

1 2 8

37