CF1175D Array Splitting

You are given an array $ a_1, a_2, \dots, a_n $ and an integer $ k $ . You are asked to divide this array into $ k $ non-empty consecutive subarrays. Every element in the array should be included in exactly one subarray. Let $ f(i) $ be the index of subarray the $ i $ -th element belongs to. Subarrays are numbered from left to right and from $ 1 $ to $ k $ . Let the cost of division be equal to $ \sum\limits_{i=1}^{n} (a_i \cdot f(i)) $ . For example, if $ a = [1, -2, -3, 4, -5, 6, -7] $ and we divide it into $ 3 $ subbarays in the following way: $ [1, -2, -3], [4, -5], [6, -7] $ , then the cost of division is equal to $ 1 \cdot 1 - 2 \cdot 1 - 3 \cdot 1 + 4 \cdot 2 - 5 \cdot 2 + 6 \cdot 3 - 7 \cdot 3 = -9 $ . Calculate the maximum cost you can obtain by dividing the array $ a $ into $ k $ non-empty consecutive subarrays.

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