Fibonacci Between

Limits 1s, 512 MB

Given two numbers $L$ and $R$ , you must print all the Fibonacci numbers between $L$ and $R$ (inclusive).

Although the number 1 appears twice in the sequence, print it only once if it falls in the given range.

You can generate the Fibonacci sequence by starting with 0 and 1. And then, add the last two numbers in the sequence every time to generate the following number.

For example:

$0 + 1 = 1$
$1 + 1 = 2$
$1 + 2 = 3$
$2 + 3 = 5$
And so on.

Input

The input will contain two integers: $L$ and $R$ ( $0 \le L < R \le 10^7$ ). The input will be such that at least one Fibonacci number will be within this range.

Output

Print all Fibonacci numbers between $L$ and $R$ (inclusive).

Sample

Input	Output
0 10	0 1 2 3 5 8
The numbers 0, 1, 2, 3, 5, 8 are part of the Fibonacci sequence and fall in the range $[0, 10]$ .