English · Original
Chinese · Translation
Formal · Original
Imp is really pleased that you helped him. But it you solve the last problem, his gladness would raise even more.
<center></center>Let's define for some set of integers as the number of pairs _a_, _b_ in , such that:
* _a_ is **strictly less** than _b_;
* _a_ **divides** _b_ without a remainder.
You are to find such a set , which is a subset of {1, 2, ..., _n_} (the set that contains all positive integers not greater than _n_), that .
## Input
The only line contains two integers _n_ and _k_ .
## Output
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 you have found, in the second line print _m_ integers — the elements of the set , in any order.
If there are multiple answers, print any of them.
[samples]
## Note
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, .
In the third example, the valid pairs in the output set are (2, 4), (4, 8), (2, 8). Thus, .
Imp 对你帮助他感到非常高兴。但如果你能解决最后一个问题，他的喜悦还会进一步提升。
你需要找到一个集合，它是 #cf_span[{1, 2, ..., n}] 的子集（即包含所有不超过 #cf_span[n] 的正整数的集合），使得其交错和等于 #cf_span[k]。
输入仅包含一行，包含两个整数 #cf_span[n] 和 #cf_span[k]。
如果无解，请输出 "_No_"。
否则，在第一行输出 "_Yes_"，第二行输出一个整数 #cf_span[m]，表示你找到的集合的大小；在第三行输出 #cf_span[m] 个整数——即该集合的元素，顺序任意。
如果存在多个答案，输出任意一个即可。
在第二个样例中，输出集合中的合法数对为 #cf_span[(1, 2)], #cf_span[(1, 4)], #cf_span[(1, 5)], #cf_span[(1, 6)], #cf_span[(2, 4)], #cf_span[(2, 6)]。因此，交错和为 #cf_span[k]。
在第三个样例中，输出集合中的合法数对为 #cf_span[(2, 4)], #cf_span[(4, 8)], #cf_span[(2, 8)]。因此，交错和为 #cf_span[k]。
## Input
输入仅包含一行，包含两个整数 #cf_span[n] 和 #cf_span[k]。
## Output
如果无解，请输出 "_No_"。否则，在第一行输出 "_Yes_"，第二行输出一个整数 #cf_span[m]，表示你找到的集合的大小；在第三行输出 #cf_span[m] 个整数——即该集合的元素，顺序任意。如果存在多个答案，输出任意一个即可。
[samples]
## Note
在第二个样例中，输出集合中的合法数对为 #cf_span[(1, 2)], #cf_span[(1, 4)], #cf_span[(1, 5)], #cf_span[(1, 6)], #cf_span[(2, 4)], #cf_span[(2, 6)]。因此，交错和为 #cf_span[k]。
在第三个样例中，输出集合中的合法数对为 #cf_span[(2, 4)], #cf_span[(4, 8)], #cf_span[(2, 8)]。因此，交错和为 #cf_span[k]。
**Definitions**
Let $ n, k \in \mathbb{Z}^+ $.
Let $ S \subseteq \{1, 2, \dots, n\} $ be a subset.
Define $ P(S) = \left| \left\{ (a,b) \in S \times S \mid a < b \text{ and } a \mid b \right\} \right| $.
**Constraints**
$ 1 \leq n \leq 10^5 $, $ 0 \leq k \leq \binom{n}{2} $
**Objective**
Find a subset $ S \subseteq \{1, 2, \dots, n\} $ such that $ P(S) = k $.
If no such $ S $ exists, output "_No_".
Otherwise, output "_Yes_", followed by $ |S| $ and the elements of $ S $.
API Response (JSON)
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"content": "Imp 对你帮助他感到非常高兴。但如果你能解决最后一个问题，他的喜悦还会进一步提升。\n\n你需要找到一个集合，它是 #cf_span[{1, 2, ..., n}] 的子集（即包含所有不超过 #cf_span[n] 的正整数的集合），使得其交错和等于 #cf_span[k]。\n\n输入仅包含一行，包含两个整数 #cf_span[n] 和 #cf_span[k]。\n\n如果无解，请输出 \"_No_\"。\n\n...",
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