k-th Missing Positive Number

/*
 * Problem : k-th missing number.
 * Input   : n, the array, then k.
 * Output  : The number.
 * Approach: Binary search on the missing count.
 * Time    : O(log n)
 * Space   : O(1)
 * Java    : 8 or newer.
 */
import java.util.Scanner;

public class Main {
    // This method solves the task. It receives the input and returns the answer.
    static int solve(int[] a, int k) {
        // Step 1: Before index i there are a[i] - (i + 1) missing numbers. This count never goes down, so we can use binary search.
        int low = 0;
        int high = a.length;
        while (low < high) {
            int middle = low + (high - low) / 2;
            // Step 2: If fewer than k numbers are missing before a[middle], the answer is to the right.
            if (a[middle] - (middle + 1) < k) {
                low = middle + 1;
            } else {
                high = middle;
            }
        }
        // Step 3: "low" numbers of the array are smaller than the answer, so the answer is low + k.
        return low + k;
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int size = scanner.nextInt();
        int[] a = new int[size];
        for (int i = 0; i < size; i++) {
            a[i] = scanner.nextInt();
        }
        int k = scanner.nextInt();
        System.out.println(solve(a, k));
    }
}