Chèn giá trị vào đầu bằng dịch phải (Insert at the Front by Right Shifting)

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem

A static array has capacity $C$, meaning that it can store at most $C$ elements. It currently contains the logical sequence

Insert value $x$ at the front.

• If $n=C$, the array is full and insertion cannot be performed.
• If $n<C$, the new logical size is $n'=n+1$ and the result $b$ satisfies

Perform the insertion according to these rules.

Input

The first line contains integers $C,n,x$. If $n>0$, the second line contains $n$ integers $a_0,a_1,\ldots,a_{n-1}$.

Output

If $n=C$, print FULL. Otherwise, print the new size $n+1$ on the first line and the resulting elements on the second line.

Subtask

Subtask 1 (100 points): $1\le C\le2\cdot10^5$; $0\le n\le C$; $|x|,|a_i|\le10^9$.

Example

Input

5 3 9
1 2 3

Output

4
9 1 2 3

Explanation

Since $n=3<C=5$, free capacity exists. The three old elements shift one position to the right, then $9$ is written at index $0$.