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<p>You are given an integer <code>n</code> and an integer <code>p</code> in the range <code>[<font face="monospace">0</font>, n - 1]</code>. Representing a <strong>0-indexed</strong> array <code>arr</code> of length <code>n</code> where all positions are set to <code>0</code>'s, except position <code>p</code> which is set to <code>1</code>.</p>
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<p>You are also given an integer array <code>banned</code> containing some positions from the array. For the <strong>i</strong><sup><strong>th</strong></sup> position in <code>banned</code>, <code>arr[banned[i]] = 0</code>, and <code>banned[i] != p</code>.</p>
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<p>You can perform <strong>multiple</strong> operations on <code>arr</code>. In an operation, you can choose a <strong>subarray</strong> with size <code>k</code> and <strong>reverse</strong> the subarray. However, the <code>1</code> in <code>arr</code> should never go to any of the positions in <code>banned</code>. In other words, after each operation <code>arr[banned[i]]</code> <strong>remains</strong> <code>0</code>.</p>
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<p><em>Return an array</em> <code>ans</code> <em>where</em><em> for each </em><code>i</code><em> from </em><code>[0, n - 1]</code>, <code>ans[i]</code> <em>is the <strong>minimum</strong> number of reverse operations needed to bring the</em> <code>1</code> <em>to position</em> <code>i</code><em> in arr</em>, <em>or</em> <code>-1</code> <em>if it is impossible</em>.</p>
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<ul>
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<li>A <strong>subarray</strong> is a contiguous <strong>non-empty</strong> sequence of elements within an array.</li>
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<li>The values of <code>ans[i]</code> are independent for all <code>i</code>'s.</li>
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<li>The <strong>reverse </strong>of an array is an array containing the values in <strong>reverse order</strong>.</li>
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</ul>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> n = 4, p = 0, banned = [1,2], k = 4
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<strong>Output:</strong> [0,-1,-1,1]
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<strong>Explanation:</strong> In this case <code>k = 4</code> so there is only one possible reverse operation we can perform, which is reversing the whole array. Initially, 1<strong> </strong>is placed at position 0 so the amount of operations we need for position 0 is <code>0</code>. We can never place a 1 on the banned positions, so the answer for positions 1 and 2 is <code>-1</code>. Finally, with one reverse operation we can bring the 1 to index 3, so the answer for position 3 is <code>1</code>.
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> n = 5, p = 0, banned = [2,4], k = 3
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<strong>Output:</strong> [0,-1,-1,-1,-1]
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<strong>Explanation:</strong> In this case the 1 is initially at position 0, so the answer for that position is <code>0</code>. We can perform reverse operations of size 3. The 1 is currently located at position 0, so we need to reverse the subarray <code>[0, 2]</code> for it to leave that position, but reversing that subarray makes position 2 have a 1, which shouldn't happen. So, we can't move the 1 from position 0, making the result for all the other positions <code>-1</code>.
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</pre>
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<p><strong class="example">Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> n = 4, p = 2, banned = [0,1,3], k = 1
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<strong>Output:</strong> [-1,-1,0,-1]
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<strong>Explanation:</strong> In this case we can only perform reverse operations of size 1.<strong> </strong>So the 1 never changes its position.
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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 <= n <= 10<sup>5</sup></code></li>
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<li><code>0 <= p <= n - 1</code></li>
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<li><code>0 <= banned.length <= n - 1</code></li>
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<li><code>0 <= banned[i] <= n - 1</code></li>
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<li><code>1 <= k <= n </code></li>
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<li><code>banned[i] != p</code></li>
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<li>all values in <code>banned</code> are <strong>unique</strong> </li>
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</ul>
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<p>You are given an integer <code>n</code> and an integer <code>p</code> representing an array <code>arr</code> of length <code>n</code> where all elements are set to 0's, except position <code>p</code> which is set to 1. You are also given an integer array <code>banned</code> containing restricted positions. Perform the following operation on <code>arr</code>:</p>
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<ul>
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<li>Reverse a <span data-keyword="subarray-nonempty"><strong>subarray</strong></span> with size <code>k</code> if the single 1 is not set to a position in <code>banned</code>.</li>
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</ul>
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<p>Return an integer array <code>answer</code> with <code>n</code> results where the <code>i<sup>th</sup></code> result is<em> </em>the <strong>minimum</strong> number of operations needed to bring the single 1 to position <code>i</code> in <code>arr</code>, or -1 if it is impossible.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">n = 4, p = 0, banned = [1,2], k = 4</span></p>
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<p><strong>Output:</strong> <span class="example-io">[0,-1,-1,1]</span></p>
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<p><strong>Explanation:</strong></p>
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<ul>
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<li>Initially 1 is placed at position 0 so the number of operations we need for position 0 is 0.</li>
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<li>We can never place 1 on the banned positions, so the answer for positions 1 and 2 is -1.</li>
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<li>Perform the operation of size 4 to reverse the whole array.</li>
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<li>After a single operation 1 is at position 3 so the answer for position 3 is 1.</li>
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</ul>
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</div>
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<p><strong class="example">Example 2:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">n = 5, p = 0, banned = [2,4], k = 3</span></p>
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<p><strong>Output:</strong> <span class="example-io">[0,-1,-1,-1,-1]</span></p>
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<p><strong>Explanation:</strong></p>
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<ul>
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<li>Initially 1 is placed at position 0 so the number of operations we need for position 0 is 0.</li>
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<li>We cannot perform the operation on the subarray positions <code>[0, 2]</code> because position 2 is in banned.</li>
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<li>Because 1 cannot be set at position 2, it is impossible to set 1 at other positions in more operations.</li>
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</ul>
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</div>
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<p><strong class="example">Example 3:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">n = 4, p = 2, banned = [0,1,3], k = 1</span></p>
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<p><strong>Output:</strong> <span class="example-io">[-1,-1,0,-1]</span></p>
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<p><strong>Explanation:</strong></p>
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<p>Perform operations of size 1 and 1 never changes its position.</p>
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</div>
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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 <= n <= 10<sup>5</sup></code></li>
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<li><code>0 <= p <= n - 1</code></li>
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<li><code>0 <= banned.length <= n - 1</code></li>
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<li><code>0 <= banned[i] <= n - 1</code></li>
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<li><code>1 <= k <= n </code></li>
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<li><code>banned[i] != p</code></li>
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<li>all values in <code>banned</code> are <strong>unique</strong> </li>
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</ul>
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