Number of Multisets

AtCoder

IDarc107_d

Time2000ms

Memory256MB

Difficulty—

You are given two positive integers $N$ and $K$. How many multisets of rational numbers satisfy all of the following conditions? * The multiset has exactly $N$ elements and the sum of them is equal to $K$. * Each element of the multiset is one of $1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots$. In other words, each element can be represented as $\frac{1}{2^i}\ (i = 0,1,\dots)$. The answer may be large, so print it modulo $998244353$. ## Constraints * $1 \leq K \leq N \leq 3000$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ [samples]

Samples

Input #1

4 2

Output #1

2

The following two multisets satisfy all of the given conditions:

*   ${1, \frac{1}{2}, \frac{1}{4}, \frac{1}{4}}$
*   ${\frac{1}{2}, \frac{1}{2}, \frac{1}{2}, \frac{1}{2}}$

Input #2

2525 425

Output #2

687232272

API Response (JSON)

{
  "problem": {
    "name": "Number of Multisets",
    "description": {
      "content": "You are given two positive integers $N$ and $K$. How many multisets of rational numbers satisfy all of the following conditions? *   The multiset has exactly $N$ elements and the sum of them is equal",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc107_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given two positive integers $N$ and $K$. How many multisets of rational numbers satisfy all of the following conditions?\n\n*   The multiset has exactly $N$ elements and the sum of them is equal...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments