Nikita likes tasks on order statistics, for example, he can easily find the $k$\-th number in increasing order on a segment of an array. But now Nikita wonders how many segments of an array there are such that a given number $x$ is the $k$\-th number in increasing order on this segment. In other words, you should find the number of segments of a given array such that there are exactly $k$ numbers of this segment which are less than $x$.
Nikita wants to get answer for this question for each $k$ from $0$ to $n$, where $n$ is the size of the array.
## Input
The first line contains two integers $n$ and $x$ $(1 \le n \le 2 \cdot 10^5, -10^9 \le x \le 10^9)$.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ $(-10^9 \le a_i \le 10^9)$ — the given array.
## Output
Print $n+1$ integers, where the $i$\-th number is the answer for Nikita's question for $k=i-1$.
[samples]
Nikita 喜欢与顺序统计相关的题目，例如，他可以轻松地在数组的某个区间内找到按递增顺序排列的第 $k$ 个数。但现在 Nikita 想知道，有多少个数组区间满足：给定的数 $x$ 是该区间内按递增顺序排列的第 $k$ 个数。换句话说，你需要找出给定数组中满足恰好有 $k$ 个数小于 $x$ 的区间数量。
Nikita 希望对每个 $k$ 从 $0$ 到 $n$（其中 $n$ 是数组的大小）都得到这个问题的答案。
第一行包含两个整数 $n$ 和 $x$ $(1 lt.eq n lt.eq 2 dot.op 10^5, -10^9 lt.eq x lt.eq 10^9)$。
第二行包含 $n$ 个整数 $a_1, a_2, dots.h, a_n$ $(-10^9 lt.eq a_i lt.eq 10^9)$ —— 给定的数组。
请输出 $n + 1$ 个整数，其中第 $i$ 个数是 Nikita 的问题在 $k = i -1$ 时的答案。
## Input
第一行包含两个整数 $n$ 和 $x$ $(1 lt.eq n lt.eq 2 dot.op 10^5, -10^9 lt.eq x lt.eq 10^9)$。第二行包含 $n$ 个整数 $a_1, a_2, dots.h, a_n$ $(-10^9 lt.eq a_i lt.eq 10^9)$ —— 给定的数组。
## Output
请输出 $n + 1$ 个整数，其中第 $i$ 个数是 Nikita 的问题在 $k = i -1$ 时的答案。
[samples]
Let $ n $ be the size of the array, $ x $ a target value, and $ a = [a_1, a_2, \dots, a_n] $ the given array.
Define a binary array $ b $ of length $ n $, where:
$$
b_i =
\begin{cases}
1 & \text{if } a_i < x \\
0 & \text{otherwise}
\end{cases}
$$
For each segment $ [l, r] $ with $ 1 \leq l \leq r \leq n $, let $ s_{l,r} = \sum_{i=l}^r b_i $ be the number of elements in the segment strictly less than $ x $.
We are to compute, for each $ k \in \{0, 1, \dots, n\} $, the number of segments $ [l, r] $ such that $ s_{l,r} = k $.
Let $ c_k $ denote the number of segments with exactly $ k $ elements less than $ x $. Then output $ c_0, c_1, \dots, c_n $.
---
**Formal Statement:**
Given:
- Array $ a \in \mathbb{Z}^n $
- Target $ x \in \mathbb{Z} $
Define:
- $ b_i = \mathbb{1}_{a_i < x} $ for $ i = 1, \dots, n $
Objective:
For each $ k = 0, 1, \dots, n $, compute:
$$
c_k = \left| \left\{ (l, r) \in [1, n]^2 \mid l \leq r \text{ and } \sum_{i=l}^r b_i = k \right\} \right|
$$
Output: $ c_0, c_1, \dots, c_n $