Construct Alternating String

You are given two integers \(K\) and \(M\). Your task is to construct a string of length \(K\) consisting solely of the characters X and Y such that:

1. The string contains exactly \(M\) occurrences of the character X.
2. No two adjacent characters are identical.

If it is impossible to construct such a string under the given conditions, print IMPOSSIBLE instead.

For example:

• For \(K=5\) and \(M=3\), one valid answer is XYXYX.
• For \(K=5\) and \(M=4\), it is impossible, so the output should be IMPOSSIBLE.

Note: The feasibility condition can be expressed mathematically as follows: In order for a valid string to exist, it must be that \(M \leq \lceil \frac{K}{2} \rceil\).

inputFormat

The input is given in a single line from stdin containing two space-separated integers:

• K: the total length of the string to be constructed.
• M: the exact number of occurrences of the character X required in the string.

outputFormat

Output a single line to stdout containing the constructed string if it is possible to satisfy the given requirements. Otherwise, output IMPOSSIBLE.

## sample

5 3

XYXYX

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