public class StringAB {

    private static final String STR_A = "A";
    private static final String STR_B = "B";
    public static final char CHAR_B = 'B';
    public static final char CHAR_A = 'A';

    public static void main(String[] args) {
        String s = generateStringNK(5, 8);
        System.out.println(s);
        System.out.println(countABPoints(s, s.length()));
    }

    private static String generateStringNK(int N, int K){
        int aCount = N / 2;
        int bCount = N % 2 == 0 ? aCount : aCount + 1;
        int maxK = aCount * bCount;

        if (K > maxK) return "";

        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < aCount; ++i) sb.append(STR_A);
        for (int i = 0; i < bCount; ++i) sb.append(STR_B);
        String s = sb.toString();

        for (int i = countABPoints(s, N); i > K; --i) s = swapABForDecrement(s, N);

        return s;
    }

    private static int countABPoints(String s, int n) {
        int bCount = 0;
        int sum = 0;
        for (int i = n - 1; i > -1; --i) {
            if(s.charAt(i) == CHAR_A) {
                sum += bCount;
            } else {
                ++bCount;
            }
        }
        return sum;
    }

    private static String swapABForDecrement(String s, int n) {
        int index = getIndexOfAAfterLastSubstringOfB(s, n);
        char[] charArray = s.toCharArray();
        charArray[index] = CHAR_B;
        charArray[index + 1] = CHAR_A;
        return new String(charArray);
    }

    private static int getIndexOfAAfterLastSubstringOfB(String s, int n) throws IndexOutOfBoundsException {
        int indexOfLastB = getIndexOfLastB(s, n);
        while (true) {
            --indexOfLastB;
            if (s.charAt(indexOfLastB) == CHAR_A) return indexOfLastB;
        }
    }

    private static int getIndexOfLastB(String s, int n) {
        int indexOfLastB = n;
        do {
            --indexOfLastB;
        } while (s.indexOf(STR_B, indexOfLastB) == -1);
        return indexOfLastB;
    }


}