PROGRAMMING:Then don't worry
The picture below is from Sina Weibo, the Encyclopedia of British jokes - so you don't have to worry about it, no matter whether you encounter problems or not.
Bloggers call this kind of logical deduction "logical self consistency", that is, all reasoning paths starting from a certain proposition will lead the conclusion to the same final proposition (joking, don't think this is the real definition of logical self consistency...). Given a more complex logic reasoning diagram, please check whether the reasoning from one given proposition to another is "logical self consistent" and how many different reasoning paths exist. For example, in the above image, from "do you have a problem?" To "then don't worry" is a kind of "logical self consistent" reasoning. There are three different reasoning paths.
###Input format:
Input first gives two positive integers $$n $$($$1 < n / Le 500 $$) and $$M $$, which are the number of propositions and the number of reasoning, respectively. Here we assume that propositions are numbered from 1 to $$n $.
Next, $$M $$line, each line gives the reasoning relationship between a pair of propositions, that is, the number of the two propositions' S1, S2 ', indicating that' S2 'can be derived from' S1 '. The topic guarantees that there is only one reasoning relationship between any two propositions, and any proposition cannot be proved by itself (that is, the proposition itself is deduced from the proposition).
The last line gives the numbers' a, B 'of the two propositions to be tested.
###Output format:
In a row, first output the number of different inference paths from 'a' to 'B', and then output 'yes' if the inference is "logically self consistent", or' no 'if not.
The title guarantees that the output data does not exceed $$10 ^ 9 $.
###Input sample 1:
```in
7 8
7 6
7 4
6 5
4 1
5 2
5 3
2 1
3 1
7 1
```
###Output sample 1:
```out
3 Yes
```
###Input example 2:
```in
7 8
7 6
7 4
6 5
4 1
5 2
5 3
6 1
3 1
7 1
```
###Output example 2:
```out
3 No
```
answer：If there is no answer, please comment
Bloggers call this kind of logical deduction "logical self consistency", that is, all reasoning paths starting from a certain proposition will lead the conclusion to the same final proposition (joking, don't think this is the real definition of logical self consistency...). Given a more complex logic reasoning diagram, please check whether the reasoning from one given proposition to another is "logical self consistent" and how many different reasoning paths exist. For example, in the above image, from "do you have a problem?" To "then don't worry" is a kind of "logical self consistent" reasoning. There are three different reasoning paths.
###Input format:
Input first gives two positive integers $$n $$($$1 < n / Le 500 $$) and $$M $$, which are the number of propositions and the number of reasoning, respectively. Here we assume that propositions are numbered from 1 to $$n $.
Next, $$M $$line, each line gives the reasoning relationship between a pair of propositions, that is, the number of the two propositions' S1, S2 ', indicating that' S2 'can be derived from' S1 '. The topic guarantees that there is only one reasoning relationship between any two propositions, and any proposition cannot be proved by itself (that is, the proposition itself is deduced from the proposition).
The last line gives the numbers' a, B 'of the two propositions to be tested.
###Output format:
In a row, first output the number of different inference paths from 'a' to 'B', and then output 'yes' if the inference is "logically self consistent", or' no 'if not.
The title guarantees that the output data does not exceed $$10 ^ 9 $.
###Input sample 1:
```in
7 8
7 6
7 4
6 5
4 1
5 2
5 3
2 1
3 1
7 1
```
###Output sample 1:
```out
3 Yes
```
###Input example 2:
```in
7 8
7 6
7 4
6 5
4 1
5 2
5 3
6 1
3 1
7 1
```
###Output example 2:
```out
3 No
```
answer：If there is no answer, please comment