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1{2  "id": 3762,3  "name": "maximize-the-minimum-game-score",4  "difficulty": "Hard",5  "link": "https://leetcode.com/problems/maximize-the-minimum-game-score/",6  "date": "2025-02-02",7  "task_description": "You are given an array `points` of size `n` and an integer `m`. There is another array `gameScore` of size `n`, where `gameScore[i]` represents the score achieved at the `ith` game. Initially, `gameScore[i] == 0` for all `i`. You start at index -1, which is outside the array (before the first position at index 0). You can make **at most** `m` moves. In each move, you can either: Increase the index by 1 and add `points[i]` to `gameScore[i]`. Decrease the index by 1 and add `points[i]` to `gameScore[i]`. **Note** that the index must always remain within the bounds of the array after the first move. Return the **maximum possible minimum** value in `gameScore` after **at most** `m` moves. **Example 1:** **Input:** points = [2,4], m = 3 **Output:** 4 **Explanation:** Initially, index `i = -1` and `gameScore = [0, 0]`. Move Index gameScore Increase `i` 0 `[2, 0]` Increase `i` 1 `[2, 4]` Decrease `i` 0 `[4, 4]` The minimum value in `gameScore` is 4, and this is the maximum possible minimum among all configurations. Hence, 4 is the output. **Example 2:** **Input:** points = [1,2,3], m = 5 **Output:** 2 **Explanation:** Initially, index `i = -1` and `gameScore = [0, 0, 0]`. Move Index gameScore Increase `i` 0 `[1, 0, 0]` Increase `i` 1 `[1, 2, 0]` Decrease `i` 0 `[2, 2, 0]` Increase `i` 1 `[2, 4, 0]` Increase `i` 2 `[2, 4, 3]` The minimum value in `gameScore` is 2, and this is the maximum possible minimum among all configurations. Hence, 2 is the output. **Constraints:** `2 <= n == points.length <= 5 * 104` `1 <= points[i] <= 106` `1 <= m <= 109`",8  "test_case": [9    {10      "label": "Example 1",11      "input": "points = [2,4], m = 3",12      "output": "4 "13    },14    {15      "label": "Example 2",16      "input": "points = [1,2,3], m = 5",17      "output": "2 "18    }19  ],20  "constraints": [21    "Increase the index by 1 and add points[i] to gameScore[i].",22    "Decrease the index by 1 and add points[i] to gameScore[i].",23    "2 <= n == points.length <= 5 * 104",24    "1 <= points[i] <= 106",25    "1 <= m <= 109"26  ],27  "python_template": "class Solution(object):\n    def maxScore(self, points, m):\n        \"\"\"\n        :type points: List[int]\n        :type m: int\n        :rtype: int\n        \"\"\"\n        ",28  "java_template": "class Solution {\n    public long maxScore(int[] points, int m) {\n        \n    }\n}",29  "metadata": {30    "func_name": "maxScore"31  }32}