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def addEllipticCurve(u,v,a,p):
    '''calculates sum of points u and v of elliptic curve y^2=x^3+ax+b mod p'''
    wx,wy = 0,0
    calc = False
    if u == (0,0):
        return v
    elif v == (0,0):
        return u
    elif u == v:
        s = (3*u[0]*u[0]+a) * pow(2*u[1],-1,p)
        calc = True
    elif u[0] != v[0]:
        s = (u[1]-v[1]) * pow(u[0]-v[0],-1,p)
        calc = True
    if calc:
        wx = (s*s-u[0]-v[0]) % p
        wy = (s*(u[0]-wx)-u[1]) % p
    return wx,wy

if __name__ == '__main__':
    u = (4,2)
    u_pot = (0,0)
    for i in range(1,10):
        u_pot = addEllipticCurve(u_pot,u,4,11)
        print(f"{i} : ({u_pot[0]},{u_pot[1]})")