## Graph Theory 4

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Points: 15
Time limit: 1.0s
Memory limit: 128M

Author:
Problem type

Given a directed graph of $$N$$ nodes, $$M$$ edges, a node $$A$$, and a node $$B$$, print YES if it is possible to travel from $$A$$ to $$B$$ even if any one edge is removed from the graph, and NO otherwise. If it is impossible to travel from $$A$$ to $$B$$, print NO PATH.

#### Input Specification

The first line will contain four integers, $$N, M, A, B\ (2 \le N \le 4 \times 10^4, 1 \le M \le 10^5, 1 \le A, B \le N, A \neq B)$$.

The next $$M$$ lines will each two integers, $$a, b\ (1 \le a, b \le N, a \neq b)$$, indicating there is a path from $$a$$ to $$b$$.

#### Output Specification

Print YES if it is possible to travel from $$A$$ to $$B$$ even if any one edge is removed from the graph, and NO otherwise. If it is impossible to travel from $$A$$ to $$B$$, print NO PATH.

#### Sample Input 1

4 5 2 3
1 2
2 3
3 1
1 4
4 1

#### Sample Output 1

NO

#### Sample Input 2

4 5 1 4
1 2
2 3
1 3
2 4
3 4

#### Sample Output 2

YES

#### Sample Input 3

3 1 1 2
1 3

#### Sample Output 3

NO PATH