Insert x After the First Occurrence of y (Chèn x sau lần xuất hiện đầu tiên của y)

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem

A static array has capacity $C$ and current logical size $n$, where $1\le n\le C$. The active sequence is $a_0,\ldots,a_{n-1}$. Given integers $x$ and $y$, define

$$I=\{i\mid0\le i<n,\ a_i=y\}.$$

If $I$ is empty, leave the array unchanged. If $I$ is nonempty but $n=C$, the array is full, so leave it unchanged. Otherwise let $p=\min I$ and insert $x$ immediately after position $p$. The new size is $n+1$, with

$$b_i=a_i\ (0\le i\le p),\qquad b_{p+1}=x,\qquad b_i=a_{i-1}\ (p+2\le i\le n).$$

Print the final logical size and array.

Input

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

Output

Print the final logical size on the first line and the active array elements on the second line.

Subtask

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

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

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

Example

Input

8 6
4 2 7 2 9 5
100 2

Output

7
4 2 100 7 2 9 5

Explanation

The sample follows the mathematical definition above.