Lemon tree

Professor Oak kas a big lemon tree that produces nice lemons. However, every time that a friend visits him, he or she always asks for “a few” of them. As a result, Prof. Oak can barely enjoy his own lemons.

Tired of this situation, Prof. Oak has decided to impose a rule: When someone asks for lemons, he or she can only take a Fibonacci number of them. (Remember the definition: $F_0 = 0$ , $F_1 = 1$ , $F_n = F_{n-1} + F_{n-2}$ for $n \ge 2$ .) This way, perhaps some lemons can be saved...

The lemon tree has currently $\ell$ lemons, and a group of $m$ mathematicians visits Prof. Oak. They will collaborate to take the maximum total number of lemons. (They will share all them later.) For instance, if $\ell = 46$ and $m = 2$ , then each mathematician can ask for $F_8 = 21$ lemons, only leaving 4 lemons to Prof. Oak. It is easy to see that there is no combination for 2 mathematicians with a sum larger than 42 but not larger than 46.

Given $\ell$ and $m$ , how many lemons will Prof. Oak enjoy?

Input

Input consists of several cases, each with $\ell$ and $m$ . Assume $0 \le \ell \le 10^{18}$ and $0 \le m \le 1000$ .

Output

For every case, print the number of lemons left by the mathematicians.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T12:11:08.139Z