Womais is exploring the country of Muigleb on foot. For this purpose, Muigleb can be thought of as a collection of towns with bidirectional roads connecting some pairs of towns. Womais starts his walk in town $$$S$$$ and intends to reach the beautiful church in town $$$T$$$. Womais does not pay a lot of attention when he walks, so he may walk into the same town or walk along the same road multiple times on his journey (he may even walk through $$$S$$$ and/or $$$T$$$ multiple times before ending his journey at $$$T$$$). However, he is aware of an old Muiglebian superstition – if the total length of your journey is odd, you will be smitten by an ancient deity. Wanting to avoid such a fate at all costs, Womais would like your help to check that no matter what route he takes, he avoids the deity's wrath.
The first line of the input consists of two positive integers $$$n,m$$$ ($$$2 \leq n \leq 2\cdot10^5$$$, $$$1 \leq m \leq 2\cdot10^5$$$). The second line contains two positive integers $$$s,t$$$ ($$$1 \leq s,t \leq n$$$, $$$s \neq t$$$) describing the starting and ending towns of Womais's journey. The remaining $$$m$$$ lines each contain two positive integers $$$u,v$$$ ($$$1 \leq u,v \leq n$$$, $$$u \neq v$$$) describing a road. It is guaranteed that each pair of cities is connected by at most one road. It is also guaranteed that it is possible to get from $$$s$$$ to $$$t$$$ using the roads.
Output "Yes" (without quotes) if all walks from $$$s$$$ to $$$t$$$ have even length, and "No" (without quotes) otherwise. Here a walk of length $$$n$$$ from $$$s$$$ to $$$t$$$ is a sequence of towns $$$a_0, \ldots, a_n$$$ such that $$$a_0=s$$$, $$$a_n=t$$$, and $$$a_i$$$ is connected by a road to $$$a_{i+1}$$$ for all $$$0 \leq i \leq n-1$$$.
You can output "Yes" and "No" in any case (for example, strings "yES", "yes" and "Yes" will be recognized as a positive response).
6 52 41 22 33 41 45 6
Yes
6 61 51 66 22 33 44 26 5
No
