AB String

You are given two integers $N$ and $K$. Find a string $S$ that satisfies both conditions below.

• $S$ has length $N$ and uses only the letters 'A' and 'B'.
• Exactly $K$ pairs $(i, j)$ satisfy $0 \le i < j < N$, character $i$ of $S$ is 'A', and character $j$ of $S$ is 'B'. Positions are counted from 0.

If more than one string satisfies both conditions, find the lexicographically smallest one. In lexicographic order 'A' comes before 'B'.

The first line contains $N$ and $K$, separated by a space. ($2 \le N \le 50$, $0 \le K \le N(N-1)/2$)

Print the lexicographically smallest string $S$ that satisfies the conditions. If no such $S$ exists, print -1.