Long ago, in a quiet tower filled with bubbling cauldrons and dusty spellbooks, there lived a rather absent-minded magician. One evening, he decided to brew a Potion of Power. The potion starts with a magical potency of $$$1$$$ — modest, but full of potential.

The magician owns two ancient runes, called Rune $$$A$$$ and Rune $$$B$$$, each capable of multiplying the potion's current magical power by a fixed (nonnegative) integral factor. He does, however, have a terrible memory. He can't recall the exact values of these multipliers — only that:

• The multiplier of Rune $$$B$$$ is exactly one greater than that of Rune $$$A$$$.
• If he ever applies Rune $$$A$$$ immediately after Rune $$$B$$$, the potion reacts violently and loses all of its power (drops to zero).

Despite this risk, the magician is quite fond of experimenting. He decides to apply every possible sequence of $$$n$$$ runes, each either $$$A$$$ or $$$B$$$, to the initial potion to see what kinds of magical strengths he can obtain.

As he is tinkering with the runes, he realizes that he will have way too much potion. He is only planning to take a single sip — exactly one unit of magical power! Now he will need to store the remaining power from all experiments in his flasks.

By some strange coincidence of fate, as often happens in magic, each of his (infinitely many) flasks can hold exactly $$$n + 1$$$ units of magical power.

The magician is an orderly man; he refuses to leave any flask partially filled. So now he wonders:

Will it be possible to divide all of the leftover magical power (after taking his sip) into flasks such that no flask is partially filled, regardless of what the power multiplier of rune $$$A$$$ is?