Background

Little $\iiint$ has nothing to do with this annoying construction problem.

Problem Description

A sequence $a$ is called valid if it satisfies the following requirements:

• $a_i = -1$ or $a_i \in [1,n]$.
• For every $a_i \not= -1$, add a directed edge $a_i \to i$. The graph formed in this way has no cycles.

Now you are given an integer $x$ and a sequence $a$, where all elements of $a$ are integers in the range $[-1,n]$. Please replace every position with $a_i = 0$ by some other integer, so that $\sum\limits ^{n} _{i=1} a_i = x$ and $a$ is valid. If no such solution exists, report that there is 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, it means you were fooled, so output a string Rick. Otherwise output $n$ integers, representing the sequence $a$ after replacing all elements that are $0$.

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

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

6 14
0 1 4 0 1 4

-1 1 4 5 1 4

6 10
0 0 0 0 0 0

-1 -1 4 5 -1 4

6 6
1 1 0 0 0 0

Rick

6 40
0 0 0 0 0 0

Rick

Hint

This problem uses bundled tests.

*Special property: it is guaranteed that $\forall a_i = 0$.

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

Special Judge return value table

• Accepted. The answer is correct.
• Oops, your answer is wrong. 1 The correct answer has no solution, but the contestant output says there is a solution.
• Oops, your answer is wrong. 2 The contestant’s output has $\sum a_i \not = x$.
• Oops, your answer is wrong. 3 The contestant’s output contains $0$.
• Oops, your answer is wrong. 4 The contestant’s output contains a cycle.
• Oops, your answer is wrong. 5 While filling in the blanks, the contestant modified positions where the input has $a_i \not= 0$.

Translated by ChatGPT 5