Maximize GCD

AtCoder

IDarc126_c

Time2000ms

Memory256MB

Difficulty—

Given is a sequence of $N$ positive integers: $A = (A_1, A_2, \ldots, A_N)$. You can do the following operation on this sequence at least zero and at most $K$ times: * choose $i\in {1,2,\ldots,N}$ and add $1$ to $A_i$. Find the maximum possible value of $\gcd(A_1, A_2, \ldots, A_N)$ after your operations. ## Constraints * $2\leq N\leq 3\times 10^5$ * $1\leq K\leq 10^{18}$ * $1 \leq A_i\leq 3\times 10^5$ ## Input Input is given from Standard Input in the following format: $N$ $K$ $A_1$ $A_2$ $\ldots$ $A_N$ [samples]

Samples

Input #1

3 6
3 4 9

Output #1

5

One way to achieve $\gcd(A_1, A_2, A_3) = 5$ is as follows.

*   Do the operation with $i = 1$ twice, with $i = 2$ once, and with $i = 3$ once, for a total of four times, which is not more than $K=6$.
*   Now we have $A_1 = 5$, $A_2 = 5$, $A_3 = 10$, for which $\gcd(A_1, A_2, A_3) = 5$.

Input #2

3 4
30 10 20

Output #2

10

Doing no operation achieves $\gcd(A_1, A_2, A_3) = 10$.

Input #3

5 12345
1 2 3 4 5

Output #3

API Response (JSON)

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    "name": "Maximize GCD",
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      "content": "Given is a sequence of $N$ positive integers: $A = (A_1, A_2, \\ldots, A_N)$. You can do the following operation on this sequence at least zero and at most $K$ times: *   choose $i\\in {1,2,\\ldots,N}$ ",
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      "statement_type": "Markdown",
      "content": "Given is a sequence of $N$ positive integers: $A = (A_1, A_2, \\ldots, A_N)$. You can do the following operation on this sequence at least zero and at most $K$ times:\n\n*   choose $i\\in {1,2,\\ldots,N}$ ...",
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