Good Permutation 2

AtCoder

IDarc178_a

Time2000ms

Memory256MB

Difficulty—

You are given a positive integer $N$ and a sequence of $M$ positive integers $A = (A_{1}, A_{2}, \dots, A_{M})$. Here, all elements of $A$ are distinct integers between $1$ and $N$, inclusive. A permutation $P = (P_{1}, P_{2}, \dots, P_{N})$ of $(1, 2, \dots, N)$ is called a **good permutation** when it satisfies the following condition for all integers $i$ such that $1 \leq i \leq M$: * No contiguous subsequence of $P$ is a permutation of $(1, 2, \dots, A_{i})$. Determine whether a **good permutation** exists, and if it does, find the lexicographically smallest **good permutation**. What is lexicographical order?A sequence $S = (S_1, S_2, \ldots, S_{|S|})$ is said to be **lexicographically smaller** than a sequence $T = (T_1, T_2, \ldots, T_{|T|})$ if one of the following conditions holds. Here, $|S|$ and $|T|$ denote the lengths of $S$ and $T$, respectively. 1. $|S| \lt |T|$ and $(S_1, S_2, \ldots, S_{|S|}) = (T_1, T_2, \ldots, T_{|S|})$. 2. There exists an integer $1 \leq i \leq \min\lbrace |S|, |T| \rbrace$ such that both of the following hold: * $(S_1, S_2, \ldots, S_{i-1}) = (T_1, T_2, \ldots, T_{i-1})$. * $S_i$ is smaller than $T_i$ (as a number). ## Constraints * $1 \leq M \leq N \leq 2 \times 10^{5}$ * $1 \leq A_{i} \leq N$ * All elements of $A$ are distinct. * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $A_{1}$ $A_{2}$ $\cdots$ $A_{M}$ [samples]

Samples

Input #1

4 1
2

Output #1

1 3 2 4

For example, $(4, 2, 1, 3)$ is not a **good permutation** because it contains $(2, 1)$ as a contiguous subsequence.
Other non-**good permutations** are $(1, 2, 3, 4)$ and $(3, 4, 2, 1)$.
Some **good permutations** are $(4, 1, 3, 2)$ and $(2, 3, 4, 1)$. Among these, the lexicographically smallest one is $(1, 3, 2, 4)$, so print it separated by spaces.

Input #2

5 3
4 3 2

Output #2

1 3 4 5 2

Examples of **good permutations** include $(3, 4, 1, 5, 2)$, $(2, 4, 5, 3, 1)$, and $(4, 1, 5, 2, 3)$.
Examples of non-**good permutations** include $(1, 2, 5, 3, 4)$, $(2, 3, 4, 1, 5)$, and $(5, 3, 1, 2, 4)$.

Input #3

92 4
16 7 1 67

Output #3

\-1

If a **good permutation** does not exist, print `-1`.

Input #4

43 2
43 2

Output #4

\-1

API Response (JSON)

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