Max GCD 2

AtCoder

IDjsc2021_c

Time2000ms

Memory256MB

Difficulty—

Given are integers $A$ and $B$. Find the maximum possible value of $\gcd(x, y)$ when we choose integers $x$ and $y$ so that $A ≤ x < y ≤ B$. Here, $\gcd(x, y)$ denotes the greatest common divisor of $x$ and $y$. ## Constraints * $A$ and $B$ are integers. * $1 ≤ A < B ≤ 2 \times 10^5$ ## Input Input is given from Standard Input in the following format: $A$ $B$ [samples]

Samples

Input #1

2 4

Output #1

2

We have three ways to choose $(x, y)$ such that $A ≤ x < y ≤ B$: $(2,3), (2,4), (3,4)$, where the greatest common divisors are $1, 2, 1$, respectively, so the maximum possible value is $2$.

Input #2

199999 200000

Output #2

1

We have $\gcd(199999, 200000) = 1$.

Input #3

101 139

Output #3

API Response (JSON)

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      "content": "Given are integers $A$ and $B$. Find the maximum possible value of $\\gcd(x, y)$ when we choose integers $x$ and $y$ so that $A ≤ x < y ≤ B$.  \nHere, $\\gcd(x, y)$ denotes the greatest common divisor of...",
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