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1{2  "id": 3583,3  "name": "sorted-gcd-pair-queries",4  "difficulty": "Hard",5  "link": "https://leetcode.com/problems/sorted-gcd-pair-queries/",6  "date": "2024-09-29",7  "task_description": "You are given an integer array `nums` of length `n` and an integer array `queries`. Let `gcdPairs` denote an array obtained by calculating the GCD of all possible pairs `(nums[i], nums[j])`, where `0 <= i < j < n`, and then sorting these values in **ascending** order. For each query `queries[i]`, you need to find the element at index `queries[i]` in `gcdPairs`. Return an integer array `answer`, where `answer[i]` is the value at `gcdPairs[queries[i]]` for each query. The term `gcd(a, b)` denotes the **greatest common divisor** of `a` and `b`. **Example 1:** **Input:** nums = [2,3,4], queries = [0,2,2] **Output:** [1,2,2] **Explanation:** `gcdPairs = [gcd(nums[0], nums[1]), gcd(nums[0], nums[2]), gcd(nums[1], nums[2])] = [1, 2, 1]`. After sorting in ascending order, `gcdPairs = [1, 1, 2]`. So, the answer is `[gcdPairs[queries[0]], gcdPairs[queries[1]], gcdPairs[queries[2]]] = [1, 2, 2]`. **Example 2:** **Input:** nums = [4,4,2,1], queries = [5,3,1,0] **Output:** [4,2,1,1] **Explanation:** `gcdPairs` sorted in ascending order is `[1, 1, 1, 2, 2, 4]`. **Example 3:** **Input:** nums = [2,2], queries = [0,0] **Output:** [2,2] **Explanation:** `gcdPairs = [2]`. **Constraints:** `2 <= n == nums.length <= 105` `1 <= nums[i] <= 5 * 104` `1 <= queries.length <= 105` `0 <= queries[i] < n * (n - 1) / 2`",8  "test_case": [9    {10      "label": "Example 1",11      "input": "nums = [2,3,4], queries = [0,2,2]",12      "output": "[1,2,2] "13    },14    {15      "label": "Example 2",16      "input": "nums = [4,4,2,1], queries = [5,3,1,0]",17      "output": "[4,2,1,1] "18    },19    {20      "label": "Example 3",21      "input": "nums = [2,2], queries = [0,0]",22      "output": "[2,2] "23    }24  ],25  "constraints": [26    "2 <= n == nums.length <= 105",27    "1 <= nums[i] <= 5 * 104",28    "1 <= queries.length <= 105",29    "0 <= queries[i] < n * (n - 1) / 2"30  ],31  "python_template": "class Solution(object):\n    def gcdValues(self, nums, queries):\n        \"\"\"\n        :type nums: List[int]\n        :type queries: List[int]\n        :rtype: List[int]\n        \"\"\"\n        ",32  "java_template": "class Solution {\n    public int[] gcdValues(int[] nums, long[] queries) {\n        \n    }\n}",33  "metadata": {34    "func_name": "gcdValues"35  }36}