Problem Background

Little $\iiint$ has no relation to this annoying construction.

Problem Description

A sequence $a$ is considered valid if it meets the following criteria:
- $a_i = -1$ or $a_i \in [1, n]$.
- For each $a_i \neq -1$, the graph formed by connecting $a_i$ to $i$ does not contain any cycles.

Given an integer $x$ and a sequence $a$ where all elements are within the range $[-1, n]$, you are required to replace all $a_i = 0$ with other integers such that $\sum_{i=1}^{n} a_i = x$ and $a$ is valid. If no such solution exists, report no solution.

Input Format

The first line contains two integers $n$ and $x$.

The second line contains $n$ integers representing the sequence $a$. It is guaranteed that $\forall a_i \in [-1, n]$.

Output Format

If there is no solution, output the string Rick. Otherwise, output $n$ integers representing the sequence $a$ after replacing all $0$ elements.

Sample Input and Output

Sample Input #1

6 -6
-1 -1 -1 0 0 0

Sample Output #1

-1 -1 -1 -1 -1 -1

Sample Input #2

6 14
0 1 4 0 1 4

Sample Output #2

-1 1 4 5 1 4

Sample Input #3

6 10
0 0 0 0 0 0

Sample Output #3

-1 -1 4 5 -1 4

Sample Input #4

6 6
1 1 0 0 0 0

Sample Output #4

Rick

Sample Input #5

6 40
0 0 0 0 0 0

Sample Output #5

Rick

Notes

This problem has subtasks.

For all data, $1 \le n \le 10^5, -10^{18} \le x \le 10^{18}$.

Special Judge Return Values

• Accepted. The answer is correct.
• Oops, your answer is wrong. 1 The answer is no solution, but the player's code outputs a solution.
• Oops, your answer is wrong. 2 The sum of the player's output does not equal $x$.
• Oops, your answer is wrong. 3 The player's output contains $0$.
• Oops, your answer is wrong. 4 The player's output contains a cycle.
• Oops, your answer is wrong. 5 The player's output changes positions of $a_i \neq 0$ from the input.

见题面 Input 部分

见题面 Output 部分