Mom bought Vasya an $n$-dimensional chocolate bar, which is an $n$-dimensional cube with each side length equal to $1$. The chocolate is marked for division into segments. Along the $i$-th dimension, it can be divided by hyperplanes into $a_i$ equal parts. Thus, the chocolate is divided into a total of $a_1 \cdot a_2 \cdot \dots \cdot a_n$ segments, where the length of each segment along the $i$-th dimension is $\frac{1}{a_i}$, and consequently, the volume of each segment is $\frac{1}{a_1 a_2 \dots a_n}$.

Vasya and his friends want to cut the chocolate to obtain at least $k$ pieces, while maximizing the volume of the smallest piece. The chocolate can only be cut at the boundaries of the segments, and each cut must pass through the entire chocolate along a hyperplane involved in the formation of the segments. Only after making all the cuts does Vasya break the chocolate into pieces.

More formally, Vasya wants to choose numbers $b_1, b_2, \dots, b_n$ ($1 \le b_i \le a_i$) — the number of parts into which Vasya will cut the chocolate along each dimension. The condition $b_1 \cdot b_2 \cdot \dots \cdot b_n \ge k$ must be satisfied to obtain at least $k$ pieces after all cuts. It can be noted that with an optimal cutting strategy using these parameters, the smallest piece will contain $\frac{a_1}{b_1} \cdot \dots \cdot \frac{a_n}{b_n}$ segments, and its volume will be equal to $\left( \frac{a_1}{b_1} \cdot \dots \cdot \frac{a_n}{b_n} \right) \cdot \frac{1}{a_1 a_2 \dots a_n}$.

Vasya wants to obtain the maximum possible value of the volume of the smallest piece multiplied by $k$, that is, he wants to maximize the number $\left( \frac{a_1}{b_1} \cdot \dots \cdot \frac{a_n}{b_n} \right) \cdot \frac{1}{a_1 a_2 \dots a_n} \cdot k$. Help him with this.

Input

The first line contains two integers $n$ and $k$ ($1 \le n \le 100$, $1 \le k \le 10^7$) — the dimension of the chocolate and the number of pieces it needs to be divided into.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^7$) — the number of segments into which the chocolate is marked along each dimension.

Output

Output a single number — the maximum possible volume of the smallest piece obtained, multiplied by $k$, with an absolute or relative error of no more than $10^{-9}$.

If it is impossible to cut the chocolate into at least $k$ pieces under the given constraints, output $0$.

Examples

Input 1

1 2
5

Output 1

0.8

Input 2

2 6
5 10

Output 2

0.72

Input 3

2 7
4 4

Output 3

0.875

Input 4

2 3
4 5

Output 4

0.75

Input 5

4 444
57 179 239 2

Output 5

0.97557326850704739751

Input 6

2 5
2 2

Output 6

0

Note

In the first example, a one-dimensional chocolate bar can be divided as follows: Then the answer is $\frac{2}{5} \cdot 2 = 0.8$.

In the second example, the chocolate can be cut as follows: Then the answer is $\frac{2}{5} \cdot \frac{3}{10} \cdot 6 = 0.72$.

In the third example, the chocolate can be cut as follows: Then the answer is $\frac{2}{4} \cdot \frac{1}{4} \cdot 7 = 0.875$.

Subtasks

Figure 1. One-dimensional chocolate bar division