O(rand)

AtCoder

IDtokiomarine2020_e

Time3000ms

Memory256MB

Difficulty—

Given are $N$ pairwise distinct non-negative integers $A_1,A_2,\ldots,A_N$. Find the number of ways to choose a set of between $1$ and $K$ numbers (inclusive) from the given numbers so that the following two conditions are satisfied: * The bitwise AND of the chosen numbers is $S$. * The bitwise OR of the chosen numbers is $T$. ## Constraints * $1 \leq N \leq 50$ * $1 \leq K \leq N$ * $0 \leq A_i < 2^{18}$ * $0 \leq S < 2^{18}$ * $0 \leq T < 2^{18}$ * $A_i \neq A_j$ ($1 \leq i < j \leq N$) ## Input Input is given from Standard Input in the following format: $N$ $K$ $S$ $T$ $A_1$ $A_2$ $...$ $A_N$ [samples]

Samples

Input #1

3 3 0 3
1 2 3

Output #1

2

The conditions are satisfied when we choose ${1,2}$ or ${1,2,3}$.

Input #2

5 3 1 7
3 4 9 1 5

Output #2

Input #3

5 4 0 15
3 4 9 1 5

Output #3

API Response (JSON)

{
  "problem": {
    "name": "O(rand)",
    "description": {
      "content": "Given are $N$ pairwise distinct non-negative integers $A_1,A_2,\\ldots,A_N$. Find the number of ways to choose a set of between $1$ and $K$ numbers (inclusive) from the given numbers so that the follow",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "tokiomarine2020_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are $N$ pairwise distinct non-negative integers $A_1,A_2,\\ldots,A_N$. Find the number of ways to choose a set of between $1$ and $K$ numbers (inclusive) from the given numbers so that the follow...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments