import os

def eea(a,b):

"""Extended Euclidean Algorithm for GCD"""

v1 = [a,1,0]

v2 = [b,0,1]

while v2[0]<>0:

p = v1[0]//v2[0]

v2, v1 = map(lambda x, y: x-y,v1,[p*vi for vi in v2]), v2

return v1

def inverse(m,k):

"""

Retourne b de maniere que b*m mod k = 1, ou 0 s'il n'y a pas de solution

"""

v = eea(m,k)

return (v[0]==1)*(v[1] % k)

def crt(N,e):

"""

Theoreme des reste chinois:

N = Liste des modulo des clefs publiques

e = Exposant des clefs publiques

Chinese Remainder Theorem:

ms = list of pairwise relatively prime integers

as = remainders when x is divided by ms

(ai is 'each in as', mi 'each in ms')

The solution for x modulo M (M = product of ms) will be:

x = a1*M1*y1 + a2*M2*y2 + ... + ar*Mr*yr (mod M),

where Mi = M/mi and yi = (Mi)^-1 (mod mi) for 1 <= i <= r.

"""

M = reduce(lambda x, y: x*y,N)

Ms = [M/mi for mi in N]

ys = [inverse(Mi, mi) for Mi,mi in zip(Ms,N)]

return reduce(lambda x, y: x+y,[ai*Mi*yi for ai,Mi,yi in zip(e,Ms,ys)]) % M

def root(x,n):

"""

Fait une racine d'ordre n sur le nombre x

Finds the integer component of the n'th root of x,

an integer such that y ** n <= x < (y + 1) ** n.

"""

high = 1

while high ** n < x:

high *= 2

low = high/2

while low < high:

mid = (low + high) // 2

if low < mid and mid**n < x:

low = mid

elif high > mid and mid**n > x:

high = mid

else:

return mid

return mid + 1

e=3

N=[79608037716527910392060670707842954224114341083822168077002144855358998405023007345791355970838437273653492726857398313047195654933011803740498167538754807659255275632647165202835846338059572102420992692073303341392512490988413552501419357400503232190597741120726276250753866130679586474440949586692852365179,

58002222048141232855465758799795991260844167004589249261667816662245991955274977287082142794911572989261856156040536668553365838145271642812811609687362700843661481653274617983708937827484947856793885821586285570844274545385852401777678956217807768608457322329935290042362221502367207511491516411517438589637,

95136786745520478217269528603148282473715660891325372806774750455600642337159386952455144391867750492077191823630711097423473530235172124790951314315271310542765846789908387211336846556241994561268538528319743374290789112373774893547676601690882211706889553455962720218486395519200617695951617114702861810811]

y=[34217065803425349356447652842993191079705593197469002356250751196039765990549766822180265723173964726087016890980051189787233837925650902081362222218365748633591895514369317316450142279676583079298758397507023942377316646300547978234729578678310028626408502085957725408232168284955403531891866121828640919987,

48038542572368143315928949857213341349144690234757944150458420344577988496364306227393161112939226347074838727793761695978722074486902525121712796142366962172291716190060386128524977245133260307337691820789978610313893799675837391244062170879810270336080741790927340336486568319993335039457684586195656124176,

55139001168534905791033093049281485849516290567638780139733282880064346293967470884523842813679361232423330290836063248352131025995684341143337417237119663347561882637003640064860966432102780676449991773140407055863369179692136108534952624411669691799286623699981636439331427079183234388844722074263884842748]

F=crt(N,y)

print "F",F

intflag = root(F,e)

print "intflag",intflag

flag = hex(intflag)[2:-1].decode('hex')

print flag