Problem Scores

AtCoder

IDagc041_d

Time2000ms

Memory256MB

Difficulty—

$N$ problems have been chosen by the judges, now it's time to assign scores to them! Problem $i$ must get an integer score $A_i$ between $1$ and $N$, inclusive. The problems have already been sorted by difficulty: $A_1 \le A_2 \le \ldots \le A_N$ must hold. Different problems can have the same score, though. Being an ICPC fan, you want contestants who solve more problems to be ranked higher. That's why, for any $k$ ($1 \le k \le N-1$), you want the sum of scores of any $k$ problems to be strictly less than the sum of scores of any $k+1$ problems. How many ways to assign scores do you have? Find this number modulo the given prime $M$. ## Constraints * $2 \leq N \leq 5000$ * $9 \times 10^8 < M < 10^9$ * $M$ is a prime. * All input values are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ [samples]

Samples

Input #1

2 998244353

Output #1

3

The possible assignments are $(1, 1)$, $(1, 2)$, $(2, 2)$.

Input #2

3 998244353

Output #2

7

The possible assignments are $(1, 1, 1)$, $(1, 2, 2)$, $(1, 3, 3)$, $(2, 2, 2)$, $(2, 2, 3)$, $(2, 3, 3)$, $(3, 3, 3)$.

Input #3

6 966666661

Output #3

Input #4

96 925309799

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Problem Scores",
    "description": {
      "content": "$N$ problems have been chosen by the judges, now it's time to assign scores to them! Problem $i$ must get an integer score $A_i$ between $1$ and $N$, inclusive. The problems have already been sorted b",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc041_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "$N$ problems have been chosen by the judges, now it's time to assign scores to them!\nProblem $i$ must get an integer score $A_i$ between $1$ and $N$, inclusive. The problems have already been sorted b...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments