Cat Snuke and a Voyage

AtCoder

IDarc079_a

Time2000ms

Memory256MB

Difficulty—

In Takahashi Kingdom, there is an archipelago of $N$ islands, called Takahashi Islands. For convenience, we will call them Island $1$, Island $2$, ..., Island $N$. There are $M$ kinds of regular boat services between these islands. Each service connects two islands. The $i$\-th service connects Island $a_i$ and Island $b_i$. Cat Snuke is on Island $1$ now, and wants to go to Island $N$. However, it turned out that there is no boat service from Island $1$ to Island $N$, so he wants to know whether it is possible to go to Island $N$ by using two boat services. Help him. ## Constraints * $3 ≤ N ≤ 200$ $000$ * $1 ≤ M ≤ 200$ $000$ * $1 ≤ a_i < b_i ≤ N$ * $(a_i, b_i) \neq (1, N)$ * If $i \neq j$, $(a_i, b_i) \neq (a_j, b_j)$. ## Input Input is given from Standard Input in the following format: $N$ $M$ $a_1$ $b_1$ $a_2$ $b_2$ : $a_M$ $b_M$ [samples]

Samples

Input #1

3 2
1 2
2 3

Output #1

POSSIBLE

Input #2

Output #2

IMPOSSIBLE

You have to use three boat services to get to Island $4$.

Input #3

100000 1
1 99999

Output #3

IMPOSSIBLE

Input #4

Output #4

POSSIBLE

You can get to Island $5$ by using two boat services: Island $1$ -> Island $4$ -> Island $5$.

API Response (JSON)

{
  "problem": {
    "name": "Cat Snuke and a Voyage",
    "description": {
      "content": "In Takahashi Kingdom, there is an archipelago of $N$ islands, called Takahashi Islands. For convenience, we will call them Island $1$, Island $2$, ..., Island $N$. There are $M$ kinds of regular boat ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc079_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "In Takahashi Kingdom, there is an archipelago of $N$ islands, called Takahashi Islands. For convenience, we will call them Island $1$, Island $2$, ..., Island $N$.\nThere are $M$ kinds of regular boat ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments