2018 Multi-University, HDU Day 6

Problem A

Solved by ultmaster. 00:39 (+4)

Problem B

Solved by kblack. 02:12 (+2)

Problem C

Solved by kblack. 04:12 (+5)

Problem G

Unsolved. (-6)

Problem J

Solved by kblack. 01:01 (+1)

Problem K

Upsolved by ultmaster. (-5)

题意：$M_n(i,j) = 1 \text{ if} \binom{i}{j} \bmod p > 0 \text{ else } 0$. $F(n,k) = \sum_{i = 0}^{p^n-1}\sum_{j=0}^{p^n-1}M_n^k(i,j)$. 求 $(\sum_{n=1}^N\sum_{k=1}^K F(n,k)) \bmod (10^9 + 7)$.

题解：打表找规律，最后发现如果枚举 $k$ 的话，是一个首项为 $q=p(p+1)\cdots(p+k)/(k+1)!$，公比也为 $q$ 的等比数列。求前 $N$ 项和即可。

ultmaster: 小学生常犯错误：等比数列求和直接套公式，从来不考虑公比为 $1$ 的情况，到最后都没看出来。（差点就有贡献了啊。。。心痛。。。

Problem L

Solved by kblack. 00:23 (+)

温暖的签到。