01Sequence

AtCoder

IDabc216_g

Time2000ms

Memory256MB

Difficulty—

Consider a sequence of length $N$ consisting of `0`s and `1`s, $A=(A_1,A_2,\dots,A_N)$, that satisfies the following condition. > For every $i=1,2,\dots,M$, there are at least $X_i$ occurrences of `1` among $A_{L_i}, A_{L_i+1}, \dots, A_{R_i}$. Print one such sequence with the **fewest** number of occurrences of `1`s. There always exists a sequence that satisfies the condition under the Constraints. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $1 \leq M \leq \min(2 \times 10^5, \frac{N(N+1)}{2} )$ * $1 \leq L_i \leq R_i \leq N$ * $1 \leq X_i \leq R_i-L_i+1$ * $(L_i,R_i) \neq (L_j,R_j)$ if $i \neq j$. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $L_1$ $R_1$ $X_1$ $L_2$ $R_2$ $X_2$ $\vdots$ $L_M$ $R_M$ $X_M$ [samples]

Samples

Input #1

Output #1

0 1 1 1 0 1 

Another acceptable output is `1 1 0 1 1 0`.  
On the other hand, `0 1 1 1 1 1`, which has more than the fewest number of `1`s, is unacceptable.

Input #2

8 2
2 6 1
3 5 3

Output #2

0 0 1 1 1 0 0 0

API Response (JSON)

{
  "problem": {
    "name": "01Sequence",
    "description": {
      "content": "Consider a sequence of length $N$ consisting of `0`s and `1`s, $A=(A_1,A_2,\\dots,A_N)$, that satisfies the following condition. > For every $i=1,2,\\dots,M$, there are at least $X_i$ occurrences of `1",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc216_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Consider a sequence of length $N$ consisting of `0`s and `1`s, $A=(A_1,A_2,\\dots,A_N)$, that satisfies the following condition.\n\n> For every $i=1,2,\\dots,M$, there are at least $X_i$ occurrences of `1...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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