A long time ago in a galaxy far, far away, there was a large
interstellar trading union, consisting of many countries from
all across the galaxy. Recently, one of the countries decided
to leave the union. As a result, other countries are thinking
about leaving too, as their participation in the union is no
longer beneficial when their main trading partners are
gone.
You are a concerned citizen of country $X$, and you want to find out whether
your country will remain in the union or not. You have crafted
a list of all pairs of countries that are trading partners of
one another. If at least half of the trading partners of any
given country $Y$ leave
the union, country $Y$
will soon follow. Given this information, you now intend to
determine whether your home country will leave the union.
Input
The input starts with one line containing four space
separated integers $C$,
$P$, $X$, and $L$. These denote the total number of
countries ($2 \leq C \leq 200\,
000$), the number of trading partnerships ($1 \leq P \leq 300\, 000$), the number
of your home country ($1 \leq X
\leq C$) and finally the number of the first country to
leave, setting in motion a chain reaction with potentially
disastrous consequences ($1 \leq
L \leq C$).
This is followed by $P$
lines, each containing two space separated integers
$A_ i$ and $B_ i$ satisfying $1 \leq A_ i < B_ i \leq C$. Such a
line denotes a trade partnership between countries $A_ i$ and $B_ i$. No pair of countries is listed
more than once.
Initially, every country has at least one trading partner in
the union.
Output
For each test case, output one line containing either
“leave” or “stay”, denoting whether you home country leaves
or stays in the union.
Sample Input 1 
Sample Output 1 
4 3 4 1
2 3
2 4
1 2

stay

Sample Input 2 
Sample Output 2 
5 5 1 1
3 4
1 2
2 3
1 3
2 5

leave

Sample Input 3 
Sample Output 3 
4 5 3 1
1 2
1 3
2 3
2 4
3 4

stay

Sample Input 4 
Sample Output 4 
10 14 1 10
1 2
1 3
1 4
2 5
3 5
4 5
5 6
5 7
5 8
5 9
6 10
7 10
8 10
9 10

leave
