Hopscotch Addict

AtCoder

IDabc132_e

Time2000ms

Memory256MB

Difficulty—

Ken loves _ken-ken-pa_ (Japanese version of hopscotch). Today, he will play it on a directed graph $G$. $G$ consists of $N$ vertices numbered $1$ to $N$, and $M$ edges. The $i$\-th edge points from Vertex $u_i$ to Vertex $v_i$. First, Ken stands on Vertex $S$. He wants to reach Vertex $T$ by repeating ken-ken-pa. In one ken-ken-pa, he does the following exactly three times: follow an edge pointing from the vertex on which he is standing. Determine if he can reach Vertex $T$ by repeating ken-ken-pa. If the answer is yes, find the minimum number of ken-ken-pa needed to reach Vertex $T$. Note that visiting Vertex $T$ in the middle of a ken-ken-pa does not count as reaching Vertex $T$ by repeating ken-ken-pa. ## Constraints * $2 \leq N \leq 10^5$ * $0 \leq M \leq \min(10^5, N (N-1))$ * $1 \leq u_i, v_i \leq N(1 \leq i \leq M)$ * $u_i \neq v_i (1 \leq i \leq M)$ * If $i \neq j$, $(u_i, v_i) \neq (u_j, v_j)$. * $1 \leq S, T \leq N$ * $S \neq T$ ## Input Input is given from Standard Input in the following format: $N$ $M$ $u_1$ $v_1$ $:$ $u_M$ $v_M$ $S$ $T$ [samples]

Samples

Input #1

Output #1

2

Ken can reach Vertex $3$ from Vertex $1$ in two ken-ken-pa, as follows: $1 \rightarrow 2 \rightarrow 3 \rightarrow 4$ in the first ken-ken-pa, then $4 \rightarrow 1 \rightarrow 2 \rightarrow 3$ in the second ken-ken-pa. This is the minimum number of ken-ken-pa needed.

Input #2

Output #2

\-1

Any number of ken-ken-pa will bring Ken back to Vertex $1$, so he cannot reach Vertex $2$, though he can pass through it in the middle of a ken-ken-pa.

Input #3

2 0
1 2

Output #3

\-1

Vertex $S$ and Vertex $T$ may be disconnected.

Input #4

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Hopscotch Addict",
    "description": {
      "content": "Ken loves _ken-ken-pa_ (Japanese version of hopscotch). Today, he will play it on a directed graph $G$. $G$ consists of $N$ vertices numbered $1$ to $N$, and $M$ edges. The $i$\\-th edge points from Ve",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc132_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Ken loves _ken-ken-pa_ (Japanese version of hopscotch). Today, he will play it on a directed graph $G$. $G$ consists of $N$ vertices numbered $1$ to $N$, and $M$ edges. The $i$\\-th edge points from Ve...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments