# 2D-kromme

import math

from decimal import *
getcontext().prec = 50

ubegin = Decimal ('0.000000001')
ueinde = Decimal ('1.000000001')

aantalstappen = Decimal ('1000')
stap = (Decimal (ueinde) - Decimal (ubegin)) / Decimal (aantalstappen)

nulpunt = Decimal ('0.646027717321562')

iabegin = Decimal (nulpunt) - Decimal ('0.01')
iaeinde = Decimal (nulpunt) + Decimal ('0.01')
ibbegin = Decimal (nulpunt) - Decimal ('0.001')
ibeinde = Decimal (nulpunt) + Decimal ('0.001')

phi0 = Decimal ('0')
E = Decimal ('2.01177698018854097539')
J = Decimal ('5')
K = Decimal (E)
U = Decimal ('1') - Decimal (K) ** Decimal ('2')

a = Decimal ('1')
b = Decimal ('-1')
c = Decimal ('1') / Decimal (J) ** Decimal ('2')
d = - Decimal (U) / Decimal (J) ** Decimal ('2')

u = Decimal (ubegin)
fu = Decimal ('1') / (Decimal (a) * Decimal (u) ** Decimal ('3') + Decimal (b) * Decimal (u) ** Decimal ('2') \
 + Decimal (c) * Decimal (u) + Decimal (d)) ** Decimal ('0.5')
phi = Decimal (phi0)

while u < ueinde:

 if u > iabegin:

  stap = Decimal (stap) / Decimal ('10')
  iabegin = Decimal ('2') * Decimal (ueinde)

 if u > ibbegin:

  stap = Decimal (stap) / Decimal ('10000000')
  ibbegin = Decimal ('2') * Decimal (ueinde)

 if u > ibeinde:

  stap = Decimal (stap) * Decimal ('10000000')
  ibeinde = Decimal ('2') * Decimal (ueinde)

 if u > iaeinde:

  stap = Decimal (stap) * Decimal ('10')
  iaeinde = Decimal ('2') * Decimal (ueinde)

 u = Decimal (u) + Decimal (stap)

 fuprev = Decimal (fu)
 fu = Decimal ('1') / (Decimal (a) * Decimal (u) ** Decimal ('3') + Decimal (b) * Decimal (u) ** Decimal ('2') \
  + Decimal (c) * Decimal (u) + Decimal (d)) ** Decimal ('0.5')
 phi = Decimal (phi) + (Decimal (fuprev) + Decimal (fu)) * Decimal (stap) / Decimal ('2')
 r = Decimal ('1') / Decimal (u)
 x = Decimal (r) * Decimal (math.cos (Decimal (phi)))
 y = Decimal (r) * Decimal (math.sin (Decimal (phi)))

 print ('{:10.5e}'.format (x), '{:10.5e}'.format (y))