Count on a Tree II
题目描述You are given a tree with $N$ nodes. The tree nodes are numbered from $1$ to $N$. Each node has an integer weight. We will ask you to perform the following operation: $u$ $v$: ask for how many di
Little Pony and Lord Tirek
题目描述Lord Tirek is a centaur and the main antagonist in the season four finale episodes in the series “My Little Pony: Friendship Is Magic”. In “Twilight’s Kingdom” (Part 1), Tirek escapes from Tartaru
Little Pony and Elements of Harmony
题目描述The Elements of Harmony are six supernatural artifacts representing subjective aspects of harmony. They are arguably the most powerful force in Equestria. The inside of Elements of Harmony can be
The Sum of Unitary Divisors
题目描述A natural number $d$ is a unitary divisor of $n$ if $d$ is a divisor of $n$ and if $d$ and ${n \over d}$ are coprime. Let $\sigma^{\ast}(n)$ be the sum of the unitary divisors of $n$. For example,
Counting Divisors (Square)
题目描述Let $\sigma_0(n)$ be the number of positive divisors of $n$. For example, $\sigma_0(1)=1, \ \sigma_0(2)=2$ and $\sigma_0(6)=4$. Let $S_2(n)=\sum_{i=1}^n \sigma_0(i^2)$. Gi
GCD Extreme (Hard)
题目描述Let $G(n)=\sum_{i=1}^n \sum_{j=i+1}^n (i, j)$.For example, $G(1)=0, \ G(2)=(1, 2)=1, \ G(3)=(1, 2)+(1, 3)+(2, 3)=3$.Given $N$, find $G(N)$ modulo $2^{64}$.
The Child and Binary Tree
题目描述Our child likes computer science very much, especially he likes binary trees. Consider the sequence of $n$ distinct positive integers: $c_1, c_2, \ldots, c_n$. The child calls a vertex-weighted ro
序列求和 V4
题意概述给定$n$和$k$，求$\sum_{i=1}^n i^k \bmod 10^9+7$。有$T$组数据。 数据范围：$1 \le T \le 500, \ 1 \le n \le 10^{18}, \ 1 \le k \le 50000$。 算法分析 1设答案为$f(n)$。这是一个$(k+1)$次多项式，只要确定$(k+2)$个点就可以确定$f$。 我们可以令$x=1\