Decayed Bridges

AtCoder

IDabc120_d

Time2000ms

Memory256MB

Difficulty—

There are $N$ islands and $M$ bridges. The $i$\-th bridge connects the $A_i$\-th and $B_i$\-th islands bidirectionally. Initially, we can travel between any two islands using some of these bridges. However, the results of a survey show that these bridges will all collapse because of aging, in the order from the first bridge to the $M$\-th bridge. Let the **inconvenience** be the number of pairs of islands $(a, b)$ ($a < b$) such that we are no longer able to travel between the $a$\-th and $b$\-th islands using some of the bridges remaining. For each $i$ $(1 \leq i \leq M)$, find the inconvenience just after the $i$\-th bridge collapses. ## Constraints * All values in input are integers. * $2 \leq N \leq 10^5$ * $1 \leq M \leq 10^5$ * $1 \leq A_i < B_i \leq N$ * All pairs $(A_i, B_i)$ are distinct. * The inconvenience is initially $0$. ## Input 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

Output #1

0
0
4
5
6

For example, when the first to third bridges have collapsed, the inconvenience is $4$ since we can no longer travel between the pairs $(1, 2), (1, 3), (2, 4)$ and $(3, 4)$.

Input #2

Output #2

Input #3

2 1
1 2

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Decayed Bridges",
    "description": {
      "content": "There are $N$ islands and $M$ bridges. The $i$\\-th bridge connects the $A_i$\\-th and $B_i$\\-th islands bidirectionally. Initially, we can travel between any two islands using some of these bridges. Ho",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc120_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ islands and $M$ bridges.\nThe $i$\\-th bridge connects the $A_i$\\-th and $B_i$\\-th islands bidirectionally.\nInitially, we can travel between any two islands using some of these bridges.\nHo...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments