Dreamoon and Sets
题意翻译
输入 $n,k$,输出 $n$ 个四元组。
满足以下条件
- 对于任意一个四元组,其中任意两个不同数的最大公约数是 $k$
- 每个数仅在所有的四元组内出现一次
要求 $n$ 个四元组内最大的数最小。
第一行输出最大的数,下面 $n$ 行输出四元组。
$1\le n\le 10000$
$1\le k\le 100$
输出四元组时,顺序和整数的顺序都不重要,你可以任意输出。
题目描述
Dreamoon likes to play with sets, integers and ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF476D/9ecd8274ff74f04a3c110790f7ff835d44a6c25f.png). ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF476D/8ea8f21b5c14716258752d62a549551fbdbf04b7.png) is defined as the largest positive integer that divides both $ a $ and $ b $ .
Let $ S $ be a set of exactly four distinct integers greater than $ 0 $ . Define $ S $ to be of rank $ k $ if and only if for all pairs of distinct elements $ s_{i} $ , $ s_{j} $ from $ S $ , ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF476D/dd0b12b681c32c8696e149f43e49ae7211e0b09c.png).
Given $ k $ and $ n $ , Dreamoon wants to make up $ n $ sets of rank $ k $ using integers from $ 1 $ to $ m $ such that no integer is used in two different sets (of course you can leave some integers without use). Calculate the minimum $ m $ that makes it possible and print one possible solution.
输入输出格式
输入格式
The single line of the input contains two space separated integers $ n $ , $ k $ ( $ 1<=n<=10000,1<=k<=100 $ ).
输出格式
On the first line print a single integer — the minimal possible $ m $ .
On each of the next $ n $ lines print four space separated integers representing the $ i $ -th set.
Neither the order of the sets nor the order of integers within a set is important. If there are multiple possible solutions with minimal $ m $ , print any one of them.
输入输出样例
输入样例 #1
1 1
输出样例 #1
5
1 2 3 5
输入样例 #2
2 2
输出样例 #2
22
2 4 6 22
14 18 10 16
说明
For the first example it's easy to see that set $ {1,2,3,4} $ isn't a valid set of rank 1 since ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF476D/b50d3b1ab922da09703e2c03eee592786ae2b8c7.png).