Lucky Five#1321

Lucky Five

1 second

64 megabytes

Very easy

Some people consider $5$ a lucky number. They throw several dice, and if $5$ appears on more than one fifth of the dice, the day is considered lucky.

There are $d i ce$ identical dice, each having $s i d es$ sides. You need to calculate the probability that the day will be lucky. The probability of rolling a $5$ on a die with $s i d es$ sides is $1/ s i d es$ .

Input

Each line is a separate test and contains the number of dice thrown, $d i ce$ ( $1 \leq d i ce \leq 20$ 1 \leq dice \leq 20), and the number of sides on each die, $s i d es$ ( $5 \leq s i d es \leq 10$ 5 \leq sides \leq 10).

Output

For each test, output in a separate line the probability that the day will be lucky. Output the probability with $6$ digits after the decimal point.

Examples

Example

3 6
5 6
5 10

0.042130
0.093225
0.006152

Example 1