def update(song_a: Song, song_b: Song, score, min_k=20):
"""
Updates the elos of song1 and song_b after match between song1 and song_b
:param song_a: first song
:param song_b: second song
:param score: score of song1, 0 for loss 1 for win
:param min_k: minimum weight of the match, to be scaled up by abnormal performance
"""
assert 0 <= score <= 1
k_a = min_k * _BONUS_BASE ** abs(song_a.calc_perf_z())
k_b = min_k * _BONUS_BASE ** abs(song_b.calc_perf_z())
print("k:", round(k_a, 1), round(k_b, 1))
exp_a = _expected(song_a.elo, song_b.elo)
exp_b = 1 - exp_a
song_a.elo = _elo(song_a.elo, exp_a, score, k_a)
song_b.elo = _elo(song_b.elo, exp_b, 1 - score, k_b)
song_a.update_recent(exp_a, score)
song_b.update_recent(exp_b, 1 - score)
