Do Not Duplicate

AtCoder

IDagc036_b

Time2000ms

Memory256MB

Difficulty—

We have a sequence of $N \times K$ integers: $X=(X_0,X_1,\cdots,X_{N \times K-1})$. Its elements are represented by another sequence of $N$ integers: $A=(A_0,A_1,\cdots,A_{N-1})$. For each pair $i, j$ ($0 \leq i \leq K-1,\ 0 \leq j \leq N-1$), $X_{i \times N + j}=A_j$ holds. Snuke has an integer sequence $s$, which is initially empty. For each $i=0,1,2,\cdots,N \times K-1$, in this order, he will perform the following operation: * If $s$ does not contain $X_i$: add $X_i$ to the end of $s$. * If $s$ does contain $X_i$: repeatedly delete the element at the end of $s$ until $s$ no longer contains $X_i$. Note that, in this case, we do **not** add $X_i$ to the end of $s$. Find the elements of $s$ after Snuke finished the operations. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $1 \leq K \leq 10^{12}$ * $1 \leq A_i \leq 2 \times 10^5$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ $A_0$ $A_1$ $\cdots$ $A_{N-1}$ [samples]

Samples

Input #1

3 2
1 2 3

Output #1

2 3

In this case, $X=(1,2,3,1,2,3)$. We will perform the operations as follows:

*   $i=0$: $s$ does not contain $1$, so we add $1$ to the end of $s$, resulting in $s=(1)$.
*   $i=1$: $s$ does not contain $2$, so we add $2$ to the end of $s$, resulting in $s=(1,2)$.
*   $i=2$: $s$ does not contain $3$, so we add $3$ to the end of $s$, resulting in $s=(1,2,3)$.
*   $i=3$: $s$ does contain $1$, so we repeatedly delete the element at the end of $s$ as long as $s$ contains $1$, which causes the following changes to $s$: $(1,2,3)→(1,2)→(1)→()$.
*   $i=4$: $s$ does not contain $2$, so we add $2$ to the end of $s$, resulting in $s=(2)$.
*   $i=5$: $s$ does not contain $3$, so we add $3$ to the end of $s$, resulting in $s=(2,3)$.

Input #2

5 10
1 2 3 2 3

Output #2

Input #3

6 1000000000000
1 1 2 2 3 3

Output #3

$s$ may be empty in the end.

Input #4

11 97
3 1 4 1 5 9 2 6 5 3 5

Output #4

9 2 6

API Response (JSON)

{
  "problem": {
    "name": "Do Not Duplicate",
    "description": {
      "content": "We have a sequence of $N \\times K$ integers: $X=(X_0,X_1,\\cdots,X_{N \\times K-1})$. Its elements are represented by another sequence of $N$ integers: $A=(A_0,A_1,\\cdots,A_{N-1})$. For each pair $i, j$",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc036_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a sequence of $N \\times K$ integers: $X=(X_0,X_1,\\cdots,X_{N \\times K-1})$. Its elements are represented by another sequence of $N$ integers: $A=(A_0,A_1,\\cdots,A_{N-1})$. For each pair $i, j$...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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