01 Balanced

AtCoder

IDagc056_c

Time5000ms

Memory256MB

Difficulty—

Consider making a string $s$ of length $N$ consisting of `0` and `1`, where $s$ must satisfy $M$ conditions. The $i$\-th condition is represented by integers $L_i$ and $R_i$ ($1 \leq L_i < R_i \leq N$). This means that there should be equal numbers of `0` and `1` between the $L_i$\-th and $R_i$\-th characters (inclusive) of $s$. Find the lexicographically smallest string $s$ that satisfies all conditions. It can be proved that the Constraints of the problem guarantee the existence of $s$ that satisfies the conditions. ## Constraints * $2 \leq N \leq 10^6$ * $1 \leq M \leq 200000$ * $1 \leq L_i < R_i \leq N$ * $(R_i-L_i+1) \equiv 0 \mod 2$ * $(L_i,R_i) \neq (L_j,R_j)$ ($i \neq j$) * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $L_1$ $R_1$ $L_2$ $R_2$ $\vdots$ $L_M$ $R_M$ [samples]

Samples

Input #1

4 2
1 2
3 4

Output #1

Input #2

6 2
1 4
3 6

Output #2

Input #3

Output #3

00100100101101001011

API Response (JSON)

{
  "problem": {
    "name": "01 Balanced",
    "description": {
      "content": "Consider making a string $s$ of length $N$ consisting of `0` and `1`, where $s$ must satisfy $M$ conditions. The $i$\\-th condition is represented by integers $L_i$ and $R_i$ ($1 \\leq L_i < R_i \\leq N$",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 5000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc056_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Consider making a string $s$ of length $N$ consisting of `0` and `1`, where $s$ must satisfy $M$ conditions. The $i$\\-th condition is represented by integers $L_i$ and $R_i$ ($1 \\leq L_i < R_i \\leq N$...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments