E. Tree Constructingtime limit per test4 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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).InputThe first line of the input contains three integers n, d and k (1 \le n, d, k \le 4 \cdot 10^5).OutputIf 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.1ExamplesInput6 3 3OutputYES3 14 11 25 22 6Input6 2 3OutputNOInput10 4 3OutputYES2 92 1010 33 16 108 24 35 66 7Input8 5 3OutputYES2 57 23 73 11 68 74 3
Input6 3 3
OutputYES3 14 11 25 22 6
['constructive algorithms', 'graphs', '*2100']