Construct Highway

AtCoder

IDabc239_f

Time2000ms

Memory256MB

Difficulty—

The Republic of Atcoder has $N$ towns numbered $1$ through $N$, and $M$ highways numbered $1$ through $M$. Highway $i$ connects Town $A_i$ and Town $B_i$ bidirectionally. King Takahashi is going to construct $(N-M-1)$ new highways so that the following two conditions are satisfied: * One can travel between every pair of towns using some number of highways * For each $i=1,\ldots,N$, exactly $D_i$ highways are directly connected to Town $i$ Determine if there is such a way of construction. If it exists, print one. ## Constraints * $2 \leq N \leq 2\times 10^5$ * $0 \leq M \lt N-1$ * $1 \leq D_i \leq N-1$ * $1\leq A_i \lt B_i \leq N$ * If $i\neq j$, then $(A_i, B_i) \neq (A_j,B_j)$. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $D_1$ $\ldots$ $D_N$ $A_1$ $B_1$ $\vdots$ $A_M$ $B_M$ [samples]

Samples

Input #1

6 2
1 2 1 2 2 2
2 3
1 4

Output #1

6 2
5 6
4 5

As in the Sample Output, the conditions can be satisfied by constructing highways connecting Towns $6$ and $2$, Towns $5$ and $6$, and Towns $4$ and $5$, respectively.
Another example to satisfy the conditions is to construct highways connecting Towns $6$ and $4$, Towns $5$ and $6$, and Towns $2$ and $5$, respectively.

Input #2

5 1
1 1 1 1 4
2 3

Output #2

\-1

Input #3

4 0
3 3 3 3

Output #3

\-1

API Response (JSON)

{
  "problem": {
    "name": "Construct Highway",
    "description": {
      "content": "The Republic of Atcoder has $N$ towns numbered $1$ through $N$, and $M$ highways numbered $1$ through $M$.   Highway $i$ connects Town $A_i$ and Town $B_i$ bidirectionally. King Takahashi is going to ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc239_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "The Republic of Atcoder has $N$ towns numbered $1$ through $N$, and $M$ highways numbered $1$ through $M$.  \nHighway $i$ connects Town $A_i$ and Town $B_i$ bidirectionally.\nKing Takahashi is going to ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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