<p>Given the <code>head</code> of a linked&nbsp;list, rotate the list to the right by <code>k</code> places.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/13/rotate1.jpg" style="width: 450px; height: 191px;" />
<pre>
<strong>Input:</strong> head = [1,2,3,4,5], k = 2
<strong>Output:</strong> [4,5,1,2,3]
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/13/roate2.jpg" style="width: 305px; height: 350px;" />
<pre>
<strong>Input:</strong> head = [0,1,2], k = 4
<strong>Output:</strong> [2,0,1]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the list is in the range <code>[0, 500]</code>.</li>
	<li><code>-100 &lt;= Node.val &lt;= 100</code></li>
	<li><code>0 &lt;= k &lt;= 2 * 10<sup>9</sup></code></li>
</ul>

class Solution:
    def rotateRight(
        self, head: Optional[ListNode], k: int
    ) -> Optional[ListNode]:
        # base cases
        if not head:
            return None
        if not head.next:
            return head

        # close the linked list into the ring
        old_tail = head
        n = 1
        while old_tail.next:
            old_tail = old_tail.next
            n += 1
        old_tail.next = head

        # find new tail : (n - k % n - 1)th node
        # and new head : (n - k % n)th node
        new_tail = head
        for i in range(n - k % n - 1):
            new_tail = new_tail.next
        new_head = new_tail.next

        # break the ring
        new_tail.next = None

        return new_head
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