There is no barrier to stop a clever girl!
This is basically a normal RSA, with some condition for the primes
\[\frac p{p+1}+\frac{q+1}q=\frac{2s-X}{s+Y}=\frac{2N+p+q+1}{N+q}\]
It’s quite unlikely that the fraction simplifies so we simply assume we have 2 equations:
\begin{align*}
2s-X &= 2N + p + q + 1\\\
s+Y &= N + q
\end{align*}
Simplifying this to solve for the primes, we get
\begin{align*}
2Y + X &= q - p + 1\\\
(2Y + X - 1)q &= q^2 - N
\end{align*}
and the quadratic can easily be solved for \(q\), thus \(p\) can also easily be solved
Since e=0x20002, we calculate m^2 by using e=0x10001, then using CRT, we compute m mod p and m mod q and find m mod N
mp = mod(m2,p).sqrt()
mq = mod(m2,q).sqrt()
m = crt([int(mp),int(mq)],[p,q])
Flag:
CCTF{4Ll___G1rL5___Are__T4len73E__:P}