CF1312D Count the Arrays

Your task is to calculate the number of arrays such that: - each array contains $ n $ elements; - each element is an integer from $ 1 $ to $ m $ ; - for each array, there is exactly one pair of equal elements; - for each array $ a $ , there exists an index $ i $ such that the array is strictly ascending before the $ i $ -th element and strictly descending after it (formally, it means that $ a_j < a_{j + 1} $ , if $ j < i $ , and $ a_j > a_{j + 1} $ , if $ j \ge i $ ).

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The arrays in the first example are: - $ [1, 2, 1] $ ; - $ [1, 3, 1] $ ; - $ [1, 4, 1] $ ; - $ [2, 3, 2] $ ; - $ [2, 4, 2] $ ; - $ [3, 4, 3] $ .