Worst Case

AtCoder

IDarc094_b

Time2000ms

Memory256MB

Difficulty—

$10^{10^{10}}$ participants, including Takahashi, competed in two programming contests. In each contest, all participants had distinct ranks from first through $10^{10^{10}}$\-th. The _score_ of a participant is the product of his/her ranks in the two contests. Process the following $Q$ queries: * In the $i$\-th query, you are given two positive integers $A_i$ and $B_i$. Assuming that Takahashi was ranked $A_i$\-th in the first contest and $B_i$\-th in the second contest, find the maximum possible number of participants whose scores are smaller than Takahashi's. ## Constraints * $1 \leq Q \leq 100$ * $1\leq A_i,B_i\leq 10^9(1\leq i\leq Q)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $Q$ $A_1$ $B_1$ $:$ $A_Q$ $B_Q$ [samples]

Samples

Input #1

8
1 4
10 5
3 3
4 11
8 9
22 40
8 36
314159265 358979323

Output #1

1
12
4
11
14
57
31
671644785

Let us denote a participant who was ranked $x$\-th in the first contest and $y$\-th in the second contest as $(x,y)$.
In the first query, $(2,1)$ is a possible candidate of a participant whose score is smaller than Takahashi's. There are never two or more participants whose scores are smaller than Takahashi's, so we should print $1$.

API Response (JSON)

{
  "problem": {
    "name": "Worst Case",
    "description": {
      "content": "$10^{10^{10}}$ participants, including Takahashi, competed in two programming contests. In each contest, all participants had distinct ranks from first through $10^{10^{10}}$\\-th. The _score_ of a par",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc094_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "$10^{10^{10}}$ participants, including Takahashi, competed in two programming contests. In each contest, all participants had distinct ranks from first through $10^{10^{10}}$\\-th.\nThe _score_ of a par...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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