Split and Insert

AtCoder

IDagc062_b

Time2000ms

Memory256MB

Difficulty—

There is a permutation $A=(A_1,A_2,\dots,A_N)$ of the integers from $1$ to $N$. Initially, we have $A_i=i\ (1\leq i \leq N)$. Takahashi will perform the following operation on this sequence $K$ times. * Choose an integer $k$ such that $0 \leq k < N$. Take the last $k$ terms of $A$ and insert them among the first $N-k$. More precisely, replace $A$ with any permutation $A'$ of the $N$ integers that satisfies the following conditions. * $(A_1,A_2,\dots,A_{N-k})$ is a (not necessarily contiguous) subsequence of $A'$. * $(A_{N-k+1},A_{N-k+2},\dots,A_{N})$ is a (not necessarily contiguous) subsequence of $A'$. The cost of the series of operations is $\sum_{i=1}^{K}k_iC_i$, where $k_i$ is the $k$ chosen in the $i$\-th operation. Takahashi wants to perform $K$ operations so that $A=(P_1,P_2,\dots,P_N)$ afterward. Determine whether it is possible to perform such a series of operations. If it is possible, find its minimum cost. ## Constraints * $2 \leq N \leq 100$ * $1 \leq K \leq 100$ * $1 \leq C_i \leq 10^9$ * $(P_1,P_2,\dots,P_N)$ is a permutation of the integers from $1$ to $N$. * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $K$ $C_1$ $C_2$ $\dots$ $C_K$ $P_1$ $P_2$ $\dots$ $P_N$ [samples]

Samples

Input #1

4 1
3
3 1 2 4

Output #1

6

By choosing $k=2$, and inserting $A_3=3$ before $A_1,A_2$ and $A_4=4$ after $A_1,A_2$, we can make $A=(3,1,2,4)$, which satisfies $A=(P_1,P_2,P_3,P_4)$. The cost of this operation is $2 \times C_1 = 6$.
It can be proved that the minimum cost of performing operations so that $A=(P_1,P_2,P_3,P_4)$ afterward is $6$.

Input #2

4 1
3
4 3 2 1

Output #2

\-1

It is impossible to perform operations so that $A=(P_1,P_2,P_3,P_4)$ afterward.

Input #3

20 10
874735445 684260477 689935252 116941558 915603029 923404262 843759669 656978932 286318130 255195090
11 15 20 10 6 8 18 2 12 4 9 13 19 3 16 7 14 17 5 1

Output #3

7372920743

API Response (JSON)

{
  "problem": {
    "name": "Split and Insert",
    "description": {
      "content": "There is a permutation $A=(A_1,A_2,\\dots,A_N)$ of the integers from $1$ to $N$. Initially, we have $A_i=i\\ (1\\leq i \\leq N)$. Takahashi will perform the following operation on this sequence $K$ times.",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc062_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a permutation $A=(A_1,A_2,\\dots,A_N)$ of the integers from $1$ to $N$. Initially, we have $A_i=i\\ (1\\leq i \\leq N)$.\nTakahashi will perform the following operation on this sequence $K$ times....",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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