Who is Saikyo?

AtCoder

IDabc313_b

Time2000ms

Memory256MB

Difficulty—

There are $N$ competitive programmers numbered person $1$, person $2$, $\ldots$, and person $N$. There is a relation called **superiority** between the programmers. For all pairs of distinct programmers $($person $X$, person $Y$$)$, exactly one of the following two relations holds: "person $X$ is stronger than person $Y$" or "person $Y$ is stronger than person $X$." The superiority is **transitive**. In other words, for all triplets of distinct programmers $($person $X$, person $Y$, person $Z$$)$, it holds that: * if person $X$ is stronger than person $Y$ and person $Y$ is stronger than person $Z$, then person $X$ is stronger than person $Z$. A person $X$ is said to be the **strongest programmer** if person $X$ is stronger than person $Y$ for all people $Y$ other than person $X$. (Under the constraints above, we can prove that there is always exactly one such person.) You have $M$ pieces of information on their superiority. The $i$\-th of them is that "person $A_i$ is stronger than person $B_i$." Can you determine the strongest programmer among the $N$ based on the information? If you can, print the person's number. Otherwise, that is, if there are multiple possible strongest programmers, print `-1`. ## Constraints * $2 \leq N \leq 50$ * $0 \leq M \leq \frac{N(N-1)}{2}$ * $1 \leq A_i, B_i \leq N$ * $A_i \neq B_i$ * If $i \neq j$, then $(A_i, B_i) \neq (A_j, B_j)$. * There is at least one way to determine superiorities for all pairs of distinct programmers, that is consistent with the given information. ## Input The input is given from Standard Input in the following format: $N$ $M$ $A_1$ $B_1$ $A_2$ $B_2$ $\vdots$ $A_M$ $B_M$ [samples]

Samples

Input #1

3 2
1 2
2 3

Output #1

1

You have two pieces of information: "person $1$ is stronger than person $2$" and "person $2$ is stronger than person $3$."  
By the transitivity, you can also infer that "person $1$ is stronger than person $3$," so person $1$ is the strongest programmer.

Input #2

3 2
1 3
2 3

Output #2

\-1

Both person $1$ and person $2$ may be the strongest programmer. Since you cannot uniquely determine which is the strongest, you should print `-1`.

Input #3

Output #3

\-1

API Response (JSON)

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    "name": "Who is Saikyo?",
    "description": {
      "content": "There are $N$ competitive programmers numbered person $1$, person $2$, $\\ldots$, and person $N$.   There is a relation called **superiority** between the programmers. For all pairs of distinct program",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc313_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ competitive programmers numbered person $1$, person $2$, $\\ldots$, and person $N$.  \nThere is a relation called **superiority** between the programmers. For all pairs of distinct program...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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