Consider the set of integers {0, 1, 2, ..., 2^n-1}. Your task is to divide it into two sets, A and B, so that the sums of k^{th }powers of elements in these sets are equal, or report that such a division is impossible.
In this problem, we assume that 0^0 = 1.
The only line of input contains two integers n and k (0 ≤ k < n ≤ 16).
If a solution exists, print 2^n letters without spaces on a single line: for each integer from 0 to 2^n-1, print the name of the set in which you put it (letter A or B). If there is more than one possible solution, print any one of them. If the division is impossible, print NO SOLUTION on a single line instead.