Favorite Interval

AtCoder

IDarc204_d

Time2000ms

Memory256MB

Difficulty—

You are given integers $N, L, R$. These integers satisfy the following: * $2 \leq N$ * $0\leq L < R \leq N$ * $(L, R)\neq (0, N)$ Initialize a length-$N$ sequence $A = (A_{0}, A_{1}, \dots , A_{N - 1})$ as $A = (0, 1, \dots, N - 1)$. Choose a permutation $P = (P_{0}, P_{1}, \dots, P_{N - (R - L) - 1})$ of $(R - L, R - L + 1, \dots , N - 1)$, and perform the following operation for $i = 0, 1, \dots N - (R - L) - 1$ in this order. * Let $a$ be the remainder when $P_{i}$ is divided by $|A|$, and remove $A_{a}$ from $A$ (after removing an element, the indices of sequence $A$ are renumbered starting from $0$). Determine whether there exists a $P$ such that $A = (L, L + 1, \dots , R - 1)$ in the end, and if it exists, output one such $P$. ## Constraints * $2\leq N\leq 2\times 10^{5}$ * $0\leq L < R\leq N$ * $(L, R) \neq (0, N)$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $L$ $R$ [samples]

Samples

Input #1

6 3 5

Output #1

Yes
2 4 5 3

When choosing $P = (2, 4, 5, 3)$, perform four operations on $A = (0, 1, 2, 3, 4, 5)$ as follows.

*   The remainder when $P_{0} = 2$ is divided by $|A| = 6$ is $2$, so remove $A_{2} = 2$ from $A$. Then, $A = (A_{0}, A_{1}, A_{2}, A_{3}, A_{4}) = (0, 1, 3, 4, 5)$.
    
*   The remainder when $P_{1} = 4$ is divided by $|A| = 5$ is $4$, so remove $A_{4} = 5$ from $A$. Then, $A = (A_{0}, A_{1}, A_{2}, A_{3}) = (0, 1, 3, 4)$.
    
*   The remainder when $P_{2} = 5$ is divided by $|A| = 4$ is $1$, so remove $A_{1} = 1$ from $A$. Then, $A = (A_{0}, A_{1}, A_{2}) = (0, 3, 4)$.
    
*   The remainder when $P_{3} = 3$ is divided by $|A| = 3$ is $0$, so remove $A_{0} = 0$ from $A$. Then, $A = (A_{0}, A_{1}) = (3, 4)$.
    

Therefore, the goal can be achieved by setting $P = (2, 4, 5, 3)$. It is also acceptable to output $P = (5, 2, 4, 3)$.

Input #2

9 2 4

Output #2

Yes
4 5 6 7 3 8 2

Input #3

178 68 167

Output #3

No

API Response (JSON)

{
  "problem": {
    "name": "Favorite Interval",
    "description": {
      "content": "You are given integers $N, L, R$. These integers satisfy the following: *   $2 \\leq N$ *   $0\\leq L < R \\leq N$ *   $(L, R)\\neq (0, N)$ Initialize a length-$N$ sequence $A = (A_{0}, A_{1}, \\dots , A",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
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    "sync_url": null,
    "sign": "arc204_d"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given integers $N, L, R$.\nThese integers satisfy the following:\n\n*   $2 \\leq N$\n*   $0\\leq L < R \\leq N$\n*   $(L, R)\\neq (0, N)$\n\nInitialize a length-$N$ sequence $A = (A_{0}, A_{1}, \\dots , A...",
      "is_translate": false,
      "language": "English"
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