There is a country of nnn cities, and the capital of this country is city 111. The cities of this country are interconnected by n1n-1n1 roads, forming a rooted tree, and the root of this tree is 111.
There is a country of nnn cities, and the capital of this country is city 111. The cities of this country are interconnected by n−1n-1n−1 roads, forming a rooted tree, and the root of this tree is 111. You are a mattress tester who is in the capital of this country right now and you are planning a trip. You have the following requirements for this trip. 1. Each city in this country is very different, so you plan to sleep in each city for exactly one night (you must sleep in a hotel in a particular city each night). 2. The distance between the cities where each of your adjacent nights are located, for time reasons, cannot exceed kkk . The distance between two cities is defined as the number of roads of a simple path between them. A simple path is a path that does not go through repeating nodes. If there is a travel option that satisfies the condition, output ``Yes`` and output the city you are in each night. Otherwise, output ``No``. Please note that you must stay in city 1 on the first night.textbf{Please note that you must stay in city 1 on the first night.}Please note that you must stay in city 1 on the first night.
