Long Shuffle

AtCoder

IDagc061_a

Time2000ms

Memory256MB

Difficulty—

There is an array $A_1, \ldots, A_N$, and initially $A_i = i$ for all $i$. Define the following routine $\mathrm{shuffle}(L, R)$: * If $R = L + 1$, swap values of $A_L$ and $A_R$ and terminate. * Otherwise, run $\mathrm{shuffle}(L, R - 1)$ followed by $\mathrm{shuffle}(L + 1, R)$. Suppose we run $\mathrm{shuffle}(1, N)$. Print the value of $A_K$ after the routine finishes. For each input file, solve $T$ test cases. ## Constraints * $1 \leq T \leq 1000$ * $2 \leq N \leq 10^{18}$ * $1 \leq K \leq N$ ## Input The input is given from Standard Input in the following format: $T$ $case_1$ $case_2$ $\vdots$ $case_T$ Each case is in the following format: $N$ $K$ [samples]

Samples

Input #1

Output #1

2
1
2
4
1
5
3

For $N=2$, we do the following and get $A=(2,1)$.

*   Run $\mathrm{shuffle}(1, 2)$, and swap $A_1$ and $A_2$.

For $N=5$, we do the following and get $A=(2,4,1,5,3)$.

*   Run $\mathrm{shuffle}(1, 5)$:
    *   Run $\mathrm{shuffle}(1, 4)$:
        *   Run $\mathrm{shuffle}(1, 3)$:
            *   $\vdots$
        *   Run $\mathrm{shuffle}(2, 4)$:
            *   $\vdots$
    *   Run $\mathrm{shuffle}(2, 5)$:
        *   Run $\mathrm{shuffle}(2, 4)$:
            *   $\vdots$
        *   Run $\mathrm{shuffle}(3, 5)$:
            *   $\vdots$

API Response (JSON)

{
  "problem": {
    "name": "Long Shuffle",
    "description": {
      "content": "There is an array $A_1, \\ldots, A_N$, and initially $A_i = i$ for all $i$. Define the following routine $\\mathrm{shuffle}(L, R)$: *   If $R = L + 1$, swap values of $A_L$ and $A_R$ and terminate. *  ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc061_a"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is an array $A_1, \\ldots, A_N$, and initially $A_i = i$ for all $i$. Define the following routine $\\mathrm{shuffle}(L, R)$:\n\n*   If $R = L + 1$, swap values of $A_L$ and $A_R$ and terminate.\n*  ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments