HA3B2

def countF1of1(poly):
    size = len(poly)
    summa = 0
    for j in range(size):
        summa += poly[j]*(1**j)

    return summa

def Fof1(poly, f1):
    size = len(poly)
    F1 = f1
    for j in range(size):
        F1 += poly[j]
    return F1

def revealMasterSecret(listOfKPoly):
    #interpolate
    #secret = sumOF(f(i)) * multiplicationssummaOF(j(j-i))
    #sumOf = 0
    secret = 0
    size = len(listOfKPoly)
    for i in range(size):
        mulOf = 1
        f =  listOfKPoly[i]
        for j in range(size):
            if j != i :
                mulOf = mulOf * (j+1)/((j+1)-(i+1))
        secret += (f * mulOf)
    return secret

def addF1InPoly(f1, poly):
    p = []
    p.append(f1)
    for i in range(len(poly)):
        p.append(poly[i])
    return p

privatepoly = [ 13, 8, 11, 1, 5]
fOf1 =  [ 75, 75, 54, 52, 77, 54, 43]
collaberationPoly = [2782, 0, 30822, 70960, 0, 256422]

f1Of1 = countF1of1(privatepoly)
fOf1 = Fof1(fOf1, f1Of1)
p = addF1InPoly(fOf1, collaberationPoly)
secret = revealMasterSecret(p)


print(f1Of1)
print(fOf1)
print(p)
print(secret)