Miles and kilometers

If you travel frequently, you may have encountered the following problem: different countries use different measurement systems. In particular, there are two main measurement systems for distances: metric and imperial. The metric system uses kilometers, while the imperial system uses miles. It is known that one mile is approximately $1.609$ kilometers. By an interesting coincidence, this value is very close to the golden ratio, which is about $1.618$. Based on this, there is an interesting method to convert distances given in miles into kilometers.

Let's consider the Fibonacci sequence: F_1 = F_2 = 1, F_n = F_{n-1} + F_{n-2} for n > 2. The ratio of two consecutive Fibonacci numbers F_{n+1}/F_n approaches the golden ratio as $n$ tends to infinity. Therefore, you can partition the number of miles into a sum of Fibonacci numbers, choosing the largest possible Fibonacci numbers. Then, for each number, switch to the next Fibonacci number and sum up the new numbers. In this way, you obtain the approximate number of kilometers.

For example, 40 \to 34 + 5 + 1 \to 55 + 8 + 2 \to 65. Thus, $40$ miles is approximately $65$ kilometers (the precise value is $64.37$ kilometers). Write a program that implements this method.