Kth Permutation Sequence

public class Solution {
    private long factorial[];

    private void getPermutationRecursively(int A,long B,int index,boolean available[],StringBuilder result) {
        if(index == A+1) {
            return;
        }

        for(int i = 1;i <= A;i++) {
            if(available[i]) {
                long fact = factorial[A-index];
                B -= fact;
                if(B <= 0) {
                    result.append(i);
                    available[i] = false;
                    getPermutationRecursively(A,B+fact,(index+1),available,result);
                    return;
                }
            }
        }
    }

    public String getPermutation(int A, int B) {
        boolean available[] = new boolean[A+1];
        factorial = new long[A+1];
        factorial[0] = 1;
        factorial[1] = 1;
        for(int i = 2;i <= A;i++) {
            factorial[i] = factorial[i-1]*i;
        }

        StringBuilder result = new StringBuilder();
        Arrays.fill(available,true);
        getPermutationRecursively(A,B,1,available,result);
        return result.toString();
    }
}