K. Perpetuum Mobile

Codeforces

IDCF10018K

Time2000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

The world famous scientist Innokentiy almost finished the creation of perpetuum mobile. Its main part is the energy generator which allows the other mobile's parts work. The generator consists of two long parallel plates with n lasers on one of them and n receivers on another. The generator is considered to be working if each laser emits the beam to some receiver such that exactly one beam is emitted to each receiver. It is obvious that some beams emitted by distinct lasers can intersect. If two beams intersect each other, one joule of energy is released per second because of the interaction of the beams. So the more beams intersect, the more energy is released. Innokentiy noticed that if the energy generator releases exactly k joules per second, the perpetuum mobile will work up to 10 times longer. The scientist can direct any laser at any receiver, but he hasn't thought of such a construction that will give exactly the required amount of energy yet. You should help the scientist to tune up the generator. The only line contains two integers n and k (1 ≤ n ≤ 200000, ) separated by space — the number of lasers in the energy generator and the power of the generator Innokentiy wants to reach. Output n integers separated by spaces. i-th number should be equal to the number of receiver which the i-th laser should be directed at. Both lasers and receivers are numbered from 1 to n. It is guaranteed that the solution exists. If there are several solutions, you can output any of them. ## Input The only line contains two integers n and k (1 ≤ n ≤ 200000, ) separated by space — the number of lasers in the energy generator and the power of the generator Innokentiy wants to reach. ## Output Output n integers separated by spaces. i-th number should be equal to the number of receiver which the i-th laser should be directed at. Both lasers and receivers are numbered from 1 to n. It is guaranteed that the solution exists. If there are several solutions, you can output any of them. [samples]

**Definitions** Let $ n, k \in \mathbb{Z} $ with $ 1 \leq n \leq 200000 $ and $ 0 \leq k \leq \binom{n}{2} $. Let $ \sigma \in S_n $ be a permutation representing the assignment of laser $ i $ to receiver $ \sigma(i) $. **Constraints** The number of intersecting beam pairs is exactly $ k $: $$ \sum_{1 \leq i < j \leq n} \mathbf{1}_{\{\sigma(i) > \sigma(j)\}} = k $$ **Objective** Find any permutation $ \sigma = (\sigma(1), \sigma(2), \dots, \sigma(n)) $ such that the number of inversions in $ \sigma $ is exactly $ k $.

API Response (JSON)

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    "name": "K. Perpetuum Mobile",
    "description": {
      "content": "The world famous scientist Innokentiy almost finished the creation of perpetuum mobile. Its main part is the energy generator which allows the other mobile's parts work. The generator consists of two ",
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    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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