Esports is a form of competitive sports using video games. Dota 2 is one of the most popular competitive video games in Esports. Recently, a new video game Dota 3 was released. In Dota 3 a player can buy some relics for their hero. Relics are counters that track hero's actions and statistics in a game.

Gloria likes to play Dota 3, so she wants to buy all $n$ available relics for her favorite hero.

Relics can be bought using an in-game currency called shards. Each relic has its own price — $c_i$ shards for the $i$-th relic. A player can buy a relic using one of the following options:

• Pay $c_i$ shards to buy the $i$-th relic;
• Pay $x$ shards and randomly get one of all $n$ relics. The probability of getting a relic is the same for all $n$ relics. If a duplicate relic is received, then the relic is recycled and $\frac{x}{2}$ shards are given back to the player.

Gloria wants to buy all $n$ relics. Help her minimize the expected number of shards she spends to buy all the relics.

The first line contains two integers $n$ and $x$ ($1 \le n \le 100$; $1 \le x \le 10\,000$) — the number of relics and the cost to receive a random relic.

The second line consists of $n$ integers $c_1, c_2, \ldots, c_n$ ($x \le c_i \le 10\,000$; $\sum{c_i} \le 10\,000$) — the prices of $n$ relics.

Print a single real number — the minimum expected number of shards that Gloria must spend to buy all the relics.

The absolute or relative error should not exceed $10^{-9}$.