#!/usr/bin/ruby

######################################
#
# Marcin Woźniak
# s434812
#
#####################################

load 'modul1.rb'

def factorial(n)
    if n == 0
     return 1
    else
     return n * factorial(n-1)
    end
end

def mysqrt(x)
    return 0 if x==0
    m=x
    p=x
    loop do
      r=(m+p/m)/2
      return m if m<=r
      m=r
    end
end

def secondSqrt(n)
    return n.to_s(2).length-1
end

def divisors_of(n)
    result = []
    arr = []

    1.times do |i|
        arr[i] = Thread.new {
        counter = 100
        a = 2
            w = nwd(a,n)
            if w > 1 && w != n
                result << w
            end

            for r in 2..100
                d = nwd(betterExponentiation(a,factorial(r),n)-1,n)
                if d == n
                    break
                end

                if d != n && d > 1 && d.odd?
                    result << d
                end

                if d == 1
                    next
                end
                r = r + 1
        end
        }
    end

    arr.each {|t| t.join}
    return result.max
end

def RecoverPrimeFactors(n,e,d)
    k = d * e - 1
    v = 0 
    v0 = 0
    
    if primalityTest(k)
        puts "Prime factors not found"
        return false
    end

    t = divisors_of(k)
    s = (k/t).to_s(2).length-1
    
    a = SecureRandom.random_number(1..n)

    if reciprocal_Phi_p(a,n) > 1
        return a
    end

    v = betterExponentiation(a,t,n)

    if v == 1 % n 
        return 0 
    end

    while v != 1 % n 
        v0 = v % n
        v = betterExponentiation(v,2,n)
    end

    if v == -1 % n
        return 0 
    else
        d = reciprocal_Phi_p(v0 + 1, n)
        return d
    end
end

#n=143
n=14205142842144491469901035779943007321473952670460614909740188710462796861921791780746014298824348546889748863603913825380912304112461129061114480661500416910991853573649055897001583708234998530660447745535711467407798340361335928981312718926721467943464464347521000503179497153112764130114342341251457556854374337702225661788558784747007799183865452550277915792606190524979919835785502848268656744723582283945123371679980696891117277548547543492116459573915049465031893477375432302554045103150951955486083526016584926750095118984741954481489582827589374811855794969993254570253121737541317841105374871
e=2219702669760051625529760071259189046161364151701596790770763259600544290997125107128138578832480323854037838605599695123440903054424577956799678397891626783444723950147784407335462559143107157658471735164714153971357443698994082727673072343180069044835094856719244582969485137575845153825021391095268519544748057926663150576101990156077844973202826679622719216615756960610764785110408304311098865781072786879379296360025429207038042833064515876868608188436266546466015175298619766069707237580766787423687287858279125035537409323009740621048068813783768774814593993312720811077575752373741693972477513
d=9738454175598488918517912045396815318351885031131011603301149540233201870415928124228184903947308481461717153640402767289853198952704967449300122329014740408508653613839688094250923162490670540988214688775753190900423588412005697560323304500348114898045236656807283167901253083798426709790746938525240264995502098847606530252043043212677911465343705421183831116604350283789270965024124861992541018116786274867535581082248878546385006259988838129620903989258127062367035340066868353921340378027331177496332241490297041686454303452932424111634076797215417394272455217584601075851777273706083879476230809

puts RecoverPrimeFactors(n,e,d).inspect