The Stern-Brocot Number System

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描述：

The Stern-Brocot tree is a beautiful way for constructing the set of
all non-negative fractions ${m \over n}$ where m

and n are relatively prime. The idea is to start with two fractions

$\left(\vphantom{ {0 \over 1}, {1 \over 0} }\right.$ ${0 \over 1}$ , ${1 \over 0}$ $\left.\vphantom{ {0 \over 1}, {1 \over 0} }\right)$
and then repeat the following operation as many times as desired:

Insert
${{m+m'} \over {n+n'}}$ between two adjacent fractions

${m \over n}$ and

${m' \over n'}$ .

For example, the first step gives us one new entry between

${0 \over 1}$ and
${1 \over 0}$ ,

$\displaystyle {0 \over 1}$ , $\displaystyle {1 \over 1}$ , $\displaystyle {1 \over 0}$

and the next gives two more:

$\displaystyle {0 \over 1}$ , $\displaystyle {1 \over 2}$ , $\displaystyle {1 \over 1}$ , $\displaystyle {2 \over 1}$ , $\displaystyle {1 \over 0}$

The next gives four more:

$\displaystyle {0 \over 1}$ , $\displaystyle {1 \over 3}$ , $\displaystyle {1 \over 2}$ , $\displaystyle {2 \over 3}$ , $\displaystyle {1 \over 1}$ , $\displaystyle {3 \over 2}$ , $\displaystyle {2 \over 1}$ , $\displaystyle {3 \over 1}$ , $\displaystyle {1 \over 0}$

The entire array can be regarded as
an infinite binary tree structure whose top levels look like this-

This construction preserves order, and thus we cannot possibly get the same
fraction in two different places.

We can, in fact, regard the Stern-Brocot tree as a number system for
representing rational numbers,
because each positive, reduced fraction occurs exactly once. Let us use
the letters ``L'' and ``R'' to stand for going
down the left or right branch as we proceed from the root of the tree
to a particular fraction; then a string
of L's and R's uniquely identifies a place in the tree.
For example, LRRL means that we go left from

${1 \over 1}$
down to
${1 \over 2}$ , then right to
${2 \over 3}$ ,
then right to
${3 \over 4}$ , then left to
${5 \over 7}$ .
We can consider LRRL to be a
representation of
${5 \over 7}$ . Every positive fraction gets represented in this
way as a unique string of L's and R's.

Well, almost every fraction.
The fraction
${1 \over 1}$ corresponds to
the empty string.
We will denote it by I, since that looks something
like 1 and stands for ``identity."

In this problem, given a positive rational fraction,
represent it in the Stern-Brocot number system.

输入：

The input file contains multiple test cases. Each test case consists of a line containing two positive integers m and n, where m and n are relatively prime. The input terminates with a test case containing two 1's for m and n, and this case must not be processed.

输出：