Diameter of Graph

题意翻译

给出 $n(1\leq n \leq 10^9)$ 个点，$m(0\leq m \leq 10^9)$ 条边，一个整数$k(0\leq k\leq 10^9)$。 定义图的直径是任意两点的最短路径中最长的路径。 判断能否构成一个无向连通图，满足图的直径严格小于 $k - 1$， 并且不能连自环，重边。

题目描述

CQXYM wants to create a connected undirected graph with $ n $ nodes and $ m $ edges, and the diameter of the graph must be strictly less than $ k-1 $ . Also, CQXYM doesn't want a graph that contains self-loops or multiple edges (i.e. each edge connects two different vertices and between each pair of vertices there is at most one edge). The diameter of a graph is the maximum distance between any two nodes. The distance between two nodes is the minimum number of the edges on the path which endpoints are the two nodes. CQXYM wonders whether it is possible to create such a graph.

输入输出格式

输入格式

The input consists of multiple test cases. The first line contains an integer $ t (1 \leq t \leq 10^5) $ — the number of test cases. The description of the test cases follows. Only one line of each test case contains three integers $ n(1 \leq n \leq 10^9) $ , $ m $ , $ k $ $ (0 \leq m,k \leq 10^9) $ .

输出格式

For each test case, print YES if it is possible to create the graph, or print NO if it is impossible. You can print each letter in any case (upper or lower).

输入输出样例

输入样例 #1

5
1 0 3
4 5 3
4 6 3
5 4 1
2 1 1

输出样例 #1

YES
NO
YES
NO
NO

说明

In the first test case, the graph's diameter equal to 0. In the second test case, the graph's diameter can only be 2. In the third test case, the graph's diameter can only be 1.