public class Solution {
    /**
     * @param nums an array with positive and negative numbers
     * @param k an integer
     * @return the maximum average
     */
    public double maxAverage(int[] nums, int k) {
        // Write your code here
        double l = Integer.MAX_VALUE, r = Integer.MIN_VALUE;
        for (int i = 0; i < nums.length; ++i) {
            if (nums[i] < l)
                l = nums[i];
            if (nums[i] > r)
                r = nums[i];
        }


        while (r - l >= 1e-6) {
            double mid = (l + r) / 2.0;

            if (check_valid(nums, mid, k)) {
                l = mid;
            }
            else {
                r = mid;
            }
        }

        return l;
    }

    private boolean check_valid(int nums[], double mid, int k) {
        int n = nums.length;
        double min_pre = 0;
        double[] sum = new double[n + 1];
        sum[0] = 0;
        for (int i = 1; i <= n; ++i) {
            sum[i] = sum[i - 1] + nums[i - 1] - mid;
            if (i >= k && sum[i] - min_pre >= 0) {
                return true;
            }
            if (i >= k)
                min_pre = Math.min(min_pre, sum[i - k + 1]);
        }
        return false;
    }
}