On the island in the middle of an ocean there is a village without mirrors where very smart green-eyed and dark blue-eyed natives lives. There is a rule in the village that if somebody of the villagers understands which color his eyes are he should leave the village at the midnight of the same day “for the better life search”. From the old days it was strictly prohibited to tell the others what color their eyes are. Nobody left the village for long time, but one day a stranger wandered in and exclaimed at ones at the whole village: “There are dark blue-eyed people among you! It is a rarity!” The stranger was driven away for the custom violation but it was too late.
In several days the village got empty.
Task. Define in how many days the village will get empty if there live N green-eyed and K dark blue-eyed natives.
Streams. Input stream contains one nonnegative integer N and one positive integer K. Output stream should contain one positive integer.