Divisibility

题意翻译

对于一个数集I f(I)表示I中(a,b)的对数 满足a<b,b%a=0 找出一个所有元素都不大于n的集合I 使得f(I)=k

题目描述

Imp is really pleased that you helped him. But it you solve the last problem, his gladness would raise even more. ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF922F/80a786f701ecc7d26672fb3b926d9dbbafc0495c.png) Let's define ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF922F/473e0c7367d2c6c65b609424fc67aa6d9df96dba.png) for some set of integers ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF922F/b0118d24df19910ba6c937fa885fbcac0ee6712c.png) as the number of pairs $ a $ , $ b $ in ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF922F/b0118d24df19910ba6c937fa885fbcac0ee6712c.png), such that:- $ a $ is strictly less than $ b $ ; - $ a $ divides $ b $ without a remainder. You are to find such a set ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF922F/b0118d24df19910ba6c937fa885fbcac0ee6712c.png), which is a subset of $ {1,2,...,n} $ (the set that contains all positive integers not greater than $ n $ ), that ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF922F/8b010c35295a2181d8d3d9dae7832a9cb8742631.png).

输入输出格式

输入格式


The only line contains two integers $ n $ and $ k $ ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF922F/8abf4553781ebbfe2252497213ee6d6360c3f2f4.png).

输出格式


If there is no answer, print "No". Otherwise, in the first line print "Yes", in the second — an integer $ m $ that denotes the size of the set ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF922F/b0118d24df19910ba6c937fa885fbcac0ee6712c.png) you have found, in the second line print $ m $ integers — the elements of the set ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF922F/b0118d24df19910ba6c937fa885fbcac0ee6712c.png), in any order. If there are multiple answers, print any of them.

输入输出样例

输入样例 #1

3 3

输出样例 #1

No

输入样例 #2

6 6

输出样例 #2

Yes
5
1 2 4 5 6 

输入样例 #3

8 3

输出样例 #3

Yes
4
2 4 5 8

说明

In the second sample, the valid pairs in the output set are $ (1,2) $ , $ (1,4) $ , $ (1,5) $ , $ (1,6) $ , $ (2,4) $ , $ (2,6) $ . Thus, ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF922F/4055df47b045359cddfa03da919a728d3502ec96.png). In the third example, the valid pairs in the output set are $ (2,4) $ , $ (4,8) $ , $ (2,8) $ . Thus, ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF922F/8e639a6dd37ec9bd64a5d37b32a72070668e9569.png).