Make Divisible

AtCoder

IDarc150_b

Time2000ms

Memory256MB

Difficulty—

You are given positive integers $A$ and $B$. Find the minimum value of $X+Y$ for non-negative integers $X$ and $Y$ such that $B+Y$ is a multiple of $A+X$. You have $T$ test cases to solve. ## Constraints * $1 \leq T \leq 100$ * $1 \leq A,\ B \leq 10^9$ * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $T$ $\mathrm{case}_{1}$ $\mathrm{case}_{2}$ $\vdots$ $\mathrm{case}_{T}$ Each case is in the following format: $A$ $B$ [samples]

Samples

Input #1

5
11 23
8 16
4394 993298361
95392025 569922442
8399283 10293

Output #1

2
0
65
2429708
8388990

For the first test case, if we let $X=1$ and $Y=1$, then $B+Y=24$ will be a multiple of $A+X=12$. Here, we have $X+Y=2$, and there is no way to make $X+Y$ smaller, so the answer is $2$.
For the second test case, if we let $X=0$ and $Y=0$, then $B+Y=16$ will be a multiple of $A+X=8$.

API Response (JSON)

{
  "problem": {
    "name": "Make Divisible",
    "description": {
      "content": "You are given positive integers $A$ and $B$. Find the minimum value of $X+Y$ for non-negative integers $X$ and $Y$ such that $B+Y$ is a multiple of $A+X$. You have $T$ test cases to solve.",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc150_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given positive integers $A$ and $B$.\nFind the minimum value of $X+Y$ for non-negative integers $X$ and $Y$ such that $B+Y$ is a multiple of $A+X$.\nYou have $T$ test cases to solve.\n\n## Constra...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments