PHOJ Integer Sequence Analyzer (Bộ phân tích dãy số nguyên PHOJ)

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem

Given an integer array $a_0,\ldots,a_{n-1}$ and a target $x$, compute

the counts $N_-,N_0,N_+$ of negative, zero and positive elements,

and the target frequency

All indices are 0-based.

Input

The first line contains $n$ and $x$. The second line contains $n$ integers $a_i$.

Output

Line 1: $S$. Line 2: m M. Line 3: N_- N_0 N_+. Line 4: p q f_x.

Subtask

Subtask 1 (20 points): $1\le n\le10$, $|a_i|,|x|\le10^3$.

Subtask 2 (30 points): $1\le n\le5000$, $|a_i|,|x|\le10^6$.

Subtask 3 (50 points): $1\le n\le2\cdot10^5$, $|a_i|,|x|\le10^9$.

Example

Input

7 2
2 -1 5 0 5 -1 2

Output

12
-1 5
2 1 4
2 5 2

Explanation

The sample follows the definitions and rules above.