Lucky Numbers

AtCoder

IDabc255_e

Time4000ms

Memory256MB

Difficulty—

You are given a sequence of $N-1$ integers $S = (S_1, S_2, \ldots, S_{N-1})$, and $M$ distinct integers $X_1, X_2, \ldots, X_M$, which are called _lucky numbers_. A sequence of $N$ integers $A = (A_1, A_2, \ldots, A_N)$ satisfying the following condition is called a _good sequence_. > $A_i + A_{i+1} = S_i$ holds for every $i = 1, 2, \ldots, N-1$. Find the maximum possible number of terms that are lucky numbers in a good sequence $A$, that is, the maximum possible number of integers $i$ between $1$ and $N$ such that $A_i \in \lbrace X_1, X_2, \ldots, X_M \rbrace$. ## Constraints * $2 \leq N \leq 10^5$ * $1 \leq M \leq 10$ * $-10^9 \leq S_i \leq 10^9$ * $-10^9 \leq X_i \leq 10^9$ * $X_1 \lt X_2 \lt \cdots \lt X_M$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $S_1$ $S_2$ $\ldots$ $S_{N-1}$ $X_1$ $X_2$ $\ldots$ $X_M$ [samples]

Samples

Input #1

9 2
2 3 3 4 -4 -7 -4 -1
-1 5

Output #1

4

A good sequence $A = (3, -1, 4, -1, 5, -9, 2, -6, 5)$ contains four terms that are lucky numbers: $A_2, A_4, A_5, A_9$, which is the maximum possible count.

Input #2

20 10
-183260318 206417795 409343217 238245886 138964265 -415224774 -499400499 -313180261 283784093 498751662 668946791 965735441 382033304 177367159 31017484 27914238 757966050 878978971 73210901
-470019195 -379631053 -287722161 -231146414 -84796739 328710269 355719851 416979387 431167199 498905398

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Lucky Numbers",
    "description": {
      "content": "You are given a sequence of $N-1$ integers $S = (S_1, S_2, \\ldots, S_{N-1})$, and $M$ distinct integers $X_1, X_2, \\ldots, X_M$, which are called _lucky numbers_. A sequence of $N$ integers $A = (A_1,",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc255_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a sequence of $N-1$ integers $S = (S_1, S_2, \\ldots, S_{N-1})$, and $M$ distinct integers $X_1, X_2, \\ldots, X_M$, which are called _lucky numbers_.\nA sequence of $N$ integers $A = (A_1,...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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