2023.7.3 闲话

把 yspm 闲话二刷了一遍，似乎可以预料到过几年之后 yspm 闲话成为后人考察这段时期 hzoi 的珍贵史料。这样说同期 BOBO 如果看 yspm 闲话的话是不是就能了解这段时间 hzoi 内部情况了？这下 yspm 成内线了。

网络促进了■■■■的进步，互联网丰富了■■形式、拓宽了■■渠道，有利于■■■■的■■■、■■■、■■■、■■■……

来自昨天闲话，这句话的介词（的）左右都是并列短语，其实有点难读懂啊。Many would agree that when we think of Christmas, we probably think of gifts, Christmas trees and Santa Claus. But behind all these things lies the true meaning of Christmas: the importance of sharing and giving love and joy to people around us.

但是百度翻译能读懂，百度翻译是真的上位个体。

今天是 7 月 3 日，一年一度的 7 月第 3 天。人的一生又有几个 7 月 3 日！做点题吧，别看闲话了。

但是 6 月是小月，7 月和 8 月是大月，9 月是小月。

推歌：平凡之路 - 朴树。

昨天的 实验报告，实际上好像应该是「探索日志」这类，「」。

图：Leasier 二刷机场修建（？

people eater - Sodikken

Your delicious body heat! It's so warm inside of me!
It's too bad you don't have more meat on your tiny body
Oh, you're dying? What do you mean? You say that I can't eat
Oh but it's so good! It tastes so sweet
How dare you deprive me

Would you like to eat with me? A dinner as a family
Where we take care of each other's needs?
Yeah, that's not happening (Heh, heh)
But I'll feed you your own hands and feet
Don't worry, it's my treat

Though I've had my feast, you're not released
'Cus I'd like seconds please

There's another one in the trash
Your despair... I wonder how long it's gonna last?

I think there's something wrong with me
Why can't I just live happily?
Just the thought of giving up your meat's impossible as sleep
And I swear everytime I breathe in, I stare in disbelief, and-
I can't go without the feeling of your flesh upon my teeth
I can't retreat, no I can't even breathe, without feeling hungry

Why do you still believe in me?

And I'm baffled why you choose to stay with me
You're completely free, yet you refuse to leave

In the face of anger, you say patience before pride
While you're feeling dead inside, I'm so alive

And it's all thanks to you that I survived
Guess I'll say thank you for lending me your life!

（来自 APJifengc）

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尝试整一个 SoyTony 筛的别的例子，不过有点失败了。

Melchior

给定正整数 \(n,m\)，计算所有长度为 \(n\)，和为 \(m\) 的序列 GCD 的三次方和，对 \(1145143\) 取模 .

\(1\le n,m\le 10^{16}\) .

先枚举 GCD，令 \(f(m)\) 表示长度为 \(n\) 和为 \(m\) 且 GCD 为 \(1\) 的自然数序列个数，那么答案就是：

\[\begin{aligned}\mathrm{ans}&=\sum_{d=1}^m\sum_a[\gcd(a_1,a_2,\cdots,a_n)=d]\cdot d^3\\&=\sum_{d=1}^md^3\sum_a[\gcd(\tfrac{a_1}d,\tfrac{a_2}d,\cdots,\tfrac{a_n}d)=1]\\&=\sum_{d\mid m}d^3\cdot f\left(\dfrac md\right)\end{aligned} \]

这是 Dirichlet 卷积的形式，那么看 \(f\)，可以想到的是容斥描述递归式：

\[f(m)=\dbinom{n+m-1}m-\sum_{d\mid m\land d\neq1}f\left(\dfrac md\right) \]

到这里，问题已经结束了 .

所有过程都暴力处理，时间复杂度瓶颈在质因数分解，使用某 P 姓算法即可 .

不过是把 SoyTony 筛中的向下取整都去掉，就变得这么简单了，膜拜大神 .