P6650 "SWTR-5" Sequence

Xiao A has a sequence $a_1, a_2, \cdots, a_n$ of length $n$. He can choose an interval $[l, r]$ such that the difference between its maximum value and minimum value is at most $k$. He also needs to find $m$ **pairwise distinct integers** $p_1, p_2, \cdots, p_m$ such that: - $m$ is a positive integer. - $\prod\limits_{i=l}^r a_i = \prod\limits_{i=1}^m p_i$. That is, the product of the chosen interval equals the product of these $m$ numbers. - Each $p_i$ is a positive integer power of a prime. The sum of the numbers of divisors of these $m$ numbers is Xiao A's score. Help him find the maximum possible score.

The first line contains two integers $n, k$. The second line contains $n$ integers $a_1, a_2, \cdots, a_n$ representing the sequence.

Output one integer in a single line, the answer.

"Sample Explanation" Sample $1$: Choose the interval $[1, 2]$, then choose $p_1 = 2$, $p_2 = 3$, $p_3 = 4$, and you can reach the maximum value $7$. The solution is not unique. Sample $2$: Choose the interval $[1, 4]$, then choose $p_1 = 4$, $p_2 = 8$, $p_3 = 3$, $p_4 = 27$, and you can reach the maximum value $13$. "Constraints and Notes" **This problem uses bundled testdata**. - Subtask 1 (1 points): $n = 1$ and $a_1$ is prime. - Subtask 2 (9 points): $n = 1$. - Subtask 3 (20 points): $n \leq 10$, $a_i \leq 20$. - Subtask 4 (13 points): $n \leq 200$, $a_i \leq 200$. - Subtask 5 (17 points): $n \leq 2 \times 10^3$. - Subtask 6 (15 points): $a_i$ is prime. - Subtask 7 (25 points): no special restrictions. For $100\%$ of the testdata: $1 \leq n \leq 10^5$, $2 \leq a_i \leq 10^5$, $0 \leq k \leq 10^5$. --- "Source" [Sweet Round 05](https://www.luogu.com.cn/contest/28195) B. idea & solution: [ET2006](https://www.luogu.com.cn/user/115194). # Input Format # Output Format # Hint Translated by ChatGPT 5