/*
 * Return the index of element k within array A if present,
 * and return -1 if not found
 */
static public int BinarySearch (int [] A, int k)
{
    return BoundedBinarySearch(A, k, 0, A.length()-1);
}


/*
 * Return the index of element k within A[left]...A[right] inclusive if present,
 * and return -1 if not found
 */
static public int BoundedBinarySearch (int [] A, int k, int left, int right)
{
    if (left > right) {    /* base case:  zero size */
        return -1;
    }
    int mid = (left + right) / 2;
    if (A[mid] == k)  {
	return mid;
    }

    else if (A[mid] > k) {  /* look in left half  */
	return BoundedBinarySearch (A, x, left, mid-1);
    }	

    else {   /* A[mid] < k --- recurse on right half  */
	return BoundedBinarySearch (A, x, mid+1, right);
    }
}