PolandBall and White-Red graph

题意翻译

给定一张 $n$ 个点的完全图，你要将其中一些边染成红色，其他的边染成白色，使得去掉所有红边或所有白边以后图仍连通。 设 $dr$ 为去掉白边后图的直径，$dw$ 为去掉红边后图的直径。 请你构造出一组满足 $\min(dr,dw)=k$ 的染色方案，无解输出 $-1$。 输出方案时，你只用输出你把哪些边染成红色即可。

题目描述

PolandBall has an undirected simple graph consisting of $ n $ vertices. Unfortunately, it has no edges. The graph is very sad because of that. PolandBall wanted to make it happier, adding some red edges. Then, he will add white edges in every remaining place. Therefore, the final graph will be a clique in two colors: white and red. Colorfulness of the graph is a value $ min(d_{r},d_{w}) $ , where $ d_{r} $ is the diameter of the red subgraph and $ d_{w} $ is the diameter of white subgraph. The diameter of a graph is a largest value $ d $ such that shortest path between some pair of vertices in it is equal to $ d $ . If the graph is not connected, we consider its diameter to be -1. PolandBall wants the final graph to be as neat as possible. He wants the final colorfulness to be equal to $ k $ . Can you help him and find any graph which satisfies PolandBall's requests?

输入输出格式

输入格式

The only one input line contains two integers $ n $ and $ k $ ( $ 2<=n<=1000 $ , $ 1<=k<=1000 $ ), representing graph's size and sought colorfulness.

输出格式

If it's impossible to find a suitable graph, print -1. Otherwise, you can output any graph which fulfills PolandBall's requirements. First, output $ m $ — the number of red edges in your graph. Then, you should output $ m $ lines, each containing two integers $ a_{i} $ and $ b_{i} $ , ( $ 1<=a_{i},b_{i}<=n $ , $ a_{i}≠b_{i} $ ) which means that there is an undirected red edge between vertices $ a_{i} $ and $ b_{i} $ . Every red edge should be printed exactly once, you can print the edges and the vertices of every edge in arbitrary order. Remember that PolandBall's graph should remain simple, so no loops or multiple edges are allowed.

输入输出样例

输入样例 #1

4 1

输出样例 #1

-1

输入样例 #2

5 2

输出样例 #2

4
1 2
2 3
3 4
4 5

说明

In the first sample case, no graph can fulfill PolandBall's requirements. In the second sample case, red graph is a path from $ 1 $ to $ 5 $ . Its diameter is $ 4 $ . However, white graph has diameter $ 2 $ , because it consists of edges 1-3, 1-4, 1-5, 2-4, 2-5, 3-5.