You start with wealth w and roll a fair six-sided die n times. An even face adds its value to your wealth; an odd face subtracts it. Return the probability that your wealth is zero or below at any point during the game.

Once you are wiped out you stay wiped out, so absorb that state rather than letting wealth recover. Work forwards over the rolls, tracking the distribution of wealth among the runs still alive.

Input

w = 5
n = 3

Output

0.31018518518518523