Class Scores - Statistics on 0..10

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem

Given $n$ integer scores $0\le a_i\le10$ and a passing threshold $0\le K\le10$, compute

$$S=\sum a_i,\quad \mu=S/n,\quad \min a_i,\quad \max a_i,$$

all frequencies $f_0,\ldots,f_{10}$, and

$$P=|\{i\mid a_i\ge K\}|.$$

Print all statistics.

Input

The first line contains $n$ and $K$. The second line contains $n$ scores in $0..10$.

Output

Line 1: $S$. Line 2: $\mu$ to 2 decimals. Line 3: minimum and maximum. Line 4: $f_0,\ldots,f_{10}$. Line 5: $P$.

Subtask

Subtask 1 (20 points): $1\le n\le10$.

Subtask 2 (30 points): $1\le n\le5000$.

Subtask 3 (50 points): $1\le n\le2\cdot10^5$.

Example

Input

8 5
10 7 5 4 7 0 5 9

Output

47
5.88
0 10
1 0 0 0 1 2 0 2 0 1 1
6

Explanation

The result follows directly from the mathematical definition above.