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<p>Given an integer array <code>nums</code> and an integer <code>k</code>, modify the array in the following way:</p>
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<ul>
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<li>choose an index <code>i</code> and replace <code>nums[i]</code> with <code>-nums[i]</code>.</li>
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</ul>
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<p>You should apply this process exactly <code>k</code> times. You may choose the same index <code>i</code> multiple times.</p>
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<p>Return <em>the largest possible sum of the array after modifying it in this way</em>.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [4,2,3], k = 1
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<strong>Output:</strong> 5
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<strong>Explanation:</strong> Choose index 1 and nums becomes [4,-2,3].
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [3,-1,0,2], k = 3
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<strong>Output:</strong> 6
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<strong>Explanation:</strong> Choose indices (1, 2, 2) and nums becomes [3,1,0,2].
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [2,-3,-1,5,-4], k = 2
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<strong>Output:</strong> 13
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<strong>Explanation:</strong> Choose indices (1, 4) and nums becomes [2,3,-1,5,4].
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= nums.length <= 10<sup>4</sup></code></li>
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<li><code>-100 <= nums[i] <= 100</code></li>
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<li><code>1 <= k <= 10<sup>4</sup></code></li>
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</ul>
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