CF1593E Gardener and Tree

一棵 $n$ 个结点的树。一个人做了多次操作，在每次操作中，他删除了树的所有叶结点。叶结点指的是树中至多有一个相邻节点的结点。  如上图中所示的树。下图显示了对树进行一次操作后的结果。  注意特殊操作的情况: 1、对空树($0$ 个顶点)进行操作时不会改变它; 2、对于仅有一个顶点的树进行操作时会移除这个顶点(这个顶点被当作一个叶子); 3、对于仅有两个顶点的树进行操作时将删除两个顶点(两个顶点都被当作叶子处理)。 求 $k$ 次操作后还剩下多少个顶点?

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The first test case is considered in the statement. The second test case contains a tree of two vertices. $ 200000 $ operations are applied to it. The first one removes all two vertices, the other operations do not change the tree. In the third test case, a tree of three vertices is given. As a result of the first operation, only $ 1 $ vertex remains in it (with the index $ 2 $ ), the second operation makes the tree empty.