```
from sage.all import factor
from pwn import remote

r = remote("challs.xmas.htsp.ro", 6050)
r.recvuntil("1/100")

for i in range(100):
print(i)
r.recvuntil("gcd(x, y) = ")
g = int(r.recvuntil("\n").strip())
r.recvuntil("lcm(x, y) = ")
l = int(r.recvuntil("\n").strip())
if g==l:
r.sendline("1")
else:
_g = list(factor(g))
_l = list(factor(l))
#print(_g)
#print(_l)
count = 0
for f in _l:
if f not in _g:
count += 1
r.sendline(str(2**count))
print(r.recvuntil("\n"))

print(r.recvuntil("\n"))
print(r.recvuntil("\n"))
```