Description: You are given three integers $$$n$$$, $$$d$$$ and $$$k$$$. Your task is to construct an undirected tree on $$$n$$$ vertices with diameter $$$d$$$ and degree of each vertex at most $$$k$$$, or say that it is impossible. An undirected tree is a connected undirected graph with $$$n - 1$$$ edges. Diameter of a tree is the maximum length of a simple path (a path in which each vertex appears at most once) between all pairs of vertices of this tree. Degree of a vertex is the number of edges incident to this vertex (i.e. for a vertex $$$u$$$ it is the number of edges $$$(u, v)$$$ that belong to the tree, where $$$v$$$ is any other vertex of a tree). Input Format: The first line of the input contains three integers $$$n$$$, $$$d$$$ and $$$k$$$ ($$$1 \le n, d, k \le 4 \cdot 10^5$$$). Output Format: If there is no tree satisfying the conditions above, print only one word "NO" (without quotes). Otherwise in the first line print "YES" (without quotes), and then print $$$n - 1$$$ lines describing edges of a tree satisfying the conditions above. Vertices of the tree must be numbered from $$$1$$$ to $$$n$$$. You can print edges and vertices connected by an edge in any order. If there are multiple answers, print any of them.1 Note: None