Catowice City

Description:

Input:

The first line contains an integer $$$t$$$ ($$$1 \le t \le 100\,000$$$), the number of test cases. Then description of $$$t$$$ test cases follow, where each description is as follows:

The first line contains integers $$$n$$$ and $$$m$$$ ($$$1 \le n \le m \le 10^6$$$), the number of Catowice residents and the number of friendship pairs between residents and cats.

Each of the next $$$m$$$ lines contains integers $$$a_i$$$ and $$$b_i$$$ ($$$1 \le a_i, b_i \le n$$$), denoting that $$$a_i$$$-th resident is acquaintances with $$$b_i$$$-th cat. It's guaranteed that each pair of some resident and some cat is listed at most once.

It's guaranteed, that for every $$$i$$$ there exists a pair between $$$i$$$-th resident and $$$i$$$-th cat.

Different test cases are separated with an empty line.

It's guaranteed, that the sum of $$$n$$$ over all test cases is at most $$$10^6$$$ and that the sum of $$$m$$$ over all test cases is at most $$$10^6$$$.

Output:

For every test case print:

• "No", if it's impossible to select the jury and contestants.
• Otherwise print "Yes".

  In the second line print two integers $$$j$$$ and $$$p$$$ ($$$1 \le j$$$, $$$1 \le p$$$, $$$j + p = n$$$) — the number of jury members and the number of contest participants.

  In the third line print $$$j$$$ distinct integers from $$$1$$$ to $$$n$$$, the indices of the residents forming a jury.

  In the fourth line print $$$p$$$ distinct integers from $$$1$$$ to $$$n$$$, the indices of the cats, which will participate in the contest.

  In case there are several correct answers, print any of them.

Sample Input:

4
3 4
1 1
2 2
3 3
1 3

3 7
1 1
1 2
1 3
2 2
3 1
3 2
3 3

1 1
1 1

2 4
1 1
1 2
2 1
2 2

Sample Output:

Yes
2 1
1 3 
2 
Yes
1 2
2 
1 3 
No
No

Note:

In the first test case, we can select the first and the third resident as a jury. Both of them are not acquaintances with a second cat, so we can select it as a contestant.

In the second test case, we can select the second resident as a jury. He is not an acquaintances with a first and a third cat, so they can be selected as contestants.

In the third test case, the only resident is acquaintances with the only cat, so they can't be in the contest together. So it's not possible to make a contest with at least one jury and at least one cat.

In the fourth test case, each resident is acquaintances with every cat, so it's again not possible to make a contest with at least one jury and at least one cat.