Coprime Pair

AtCoder

IDarc137_a

Time2000ms

Memory256MB

Difficulty—

You are given integers $L,R$ ($L < R$). Snuke is looking for a pair of integers $(x,y)$ that satisfy both of the conditions below. * $L \leq x < y \leq R$ * $\gcd(x,y)=1$ Find the maximum possible value of $(y-x)$ in a pair that satisfies the conditions. It can be proved that at least one such pair exists under the Constraints. ## Constraints * $1 \leq L < R \leq 10^{18}$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $L$ $R$ [samples]

Samples

Input #1

2 4

Output #1

1

For $(x,y)=(2,4)$, we have $\gcd(x,y)=2$, which violates the condition. For $(x,y)=(2,3)$, the conditions are satisfied. Here, the value of $(y-x)$ is $1$. There is no such pair with a greater value of $(y-x)$, so the answer is $1$.

Input #2

14 21

Output #2

Input #3

1 100

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Coprime Pair",
    "description": {
      "content": "You are given integers $L,R$ ($L < R$). Snuke is looking for a pair of integers $(x,y)$ that satisfy both of the conditions below. *   $L \\leq x < y \\leq R$ *   $\\gcd(x,y)=1$ Find the maximum possib",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc137_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given integers $L,R$ ($L < R$).\nSnuke is looking for a pair of integers $(x,y)$ that satisfy both of the conditions below.\n\n*   $L \\leq x < y \\leq R$\n*   $\\gcd(x,y)=1$\n\nFind the maximum possib...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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