Chèn vào mảng tăng đã cho để vẫn tăng (Insert into a Strictly Increasing Array)

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem

Given a strictly increasing integer array

$$a_0<a_1<\cdots<a_{n-1}$$

and an integer $x$ that is different from every array element.

Insert $x$ so that the resulting array $b$ has $n+1$ elements and is still strictly increasing.

Define

$$p=\min\left(\{i\mid 0\le i<n,\ a_i>x\}\cup\{n\}\right).$$

Then $x$ must be inserted at index $p$, while old elements from $p$ onward move one position to the right.

Print the new size and the resulting array.

Input

The first line contains integers $n$ and $x$. The second line contains $n$ strictly increasing integers $a_0,a_1,\ldots,a_{n-1}$.

Output

Print $n+1$ on the first line. Print the array after inserting $x$ on the second line.

Subtask

Subtask 1 (100 points): $1\le n<2\cdot10^5$; $|a_i|,|x|\le10^9$; $a_i<a_{i+1}$; $x\ne a_i$ for every $i$.

Example

Input

5 6
1 3 5 8 10

Output

6
1 3 5 6 8 10

Explanation

The first element greater than $6$ is $8$ at index $3$, so $p=3$. Inserting $6$ before $8$ keeps the array strictly increasing.