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 $[0, 10]$.