Search in a Big Sorted Array

Given a big sorted array with positive integers sorted by ascending order. The array is so big so that you can not get the length of the whole array directly, and you can only access the kth number by ArrayReader.get(k) (or ArrayReader->get(k) for C++). Find the first index of a target number. Your algorithm should be in O(log k), where k is the first index of the target number.

    public int searchBigSortedArray(ArrayReader reader, int target) {
        // Algorithm:
        // 1. get the index that ArrayReader.get(index) >= target or == -1 in
        //    O(logk)
        // 2. Binary search the target between 0 and index

        int index = 1;
        while ( reader.get ( index - 1 ) < target && reader.get (index - 1 ) != -1){
            index = 2 * index;
        }
        int start = index / 2;
        int end = index;

        while ( start + 1 < end){
            int mid = start + (end - start ) / 2;
            if ( reader.get (mid) < target ){
                start = mid;
            }else {
                end = mid;
            }
        }

        if ( reader.get(start) == target) return start;
        else if ( reader.get(end) == target) return end;
        return -1;

    }