Median of a Row-wise Sorted Matrix

/*
 * Problem : Find the median.
 * Input   : r, c and the rows.
 * Output  : The median.
 * Approach: Binary search on the value
 * Time    : O(r log(c) log(range))
 * 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 long solve(int[][] m) {
        int rows = m.length;
        int cols = m[0].length;
        // Step 1: The median is a value between the smallest and the biggest number. Search for it with binary search on the value.
        long low = Long.MAX_VALUE;
        long high = Long.MIN_VALUE;
        for (int[] row : m) {
            low = Math.min(low, row[0]);
            high = Math.max(high, row[cols - 1]);
        }
        long wanted = (long) rows * cols / 2;
        while (low < high) {
            long mid = low + (high - low) / 2;
            // Step 2: Count how many numbers are <= mid. Every row is sorted, so a binary search per row is enough.
            long count = 0;
            for (int[] row : m) {
                int left = 0;
                int right = cols;
                while (left < right) {
                    int middle = (left + right) / 2;
                    if (row[middle] <= mid) {
                        left = middle + 1;
                    } else {
                        right = middle;
                    }
                }
                count += left;
            }
            // Step 3: The median is the smallest value with more than "wanted" numbers at or below it.
            if (count <= wanted) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low;
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int rows = scanner.nextInt();
        int cols = scanner.nextInt();
        int[][] m = new int[rows][cols];
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                m[i][j] = scanner.nextInt();
            }
        }
        System.out.println(solve(m));
    }
}