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4675：GCD of Sequence

题目描述
Alice is playing a game with Bob.
Alice shows N integers a1, a2, …, aN, and M, K. She says each integers 1 ≤ ai ≤ M.
And now Alice wants to ask for each d = 1 to M, how many different sequences b1, b2, …, bN. which satisfies :
1. For each i = 1…N, 1 ≤ b[i] ≤ M
2. gcd(b1, b2, …, bN) = d
3. There will be exactly K position i that ai != bi (1 ≤ i ≤ n)

Alice thinks that the answer will be too large. In order not to annoy Bob, she only wants to know the answer modulo 1000000007.Bob can not solve the problem. Now he asks you for HELP!
Notes: gcd(x1, x2, …, xn) is the greatest common divisor of x1, x2, …, xn
输入解释
The input contains several test cases, terminated by EOF.
The first line of each test contains three integers N, M, K. (1 ≤ N, M ≤ 300000, 1 ≤ K ≤ N)
The second line contains N integers: a1, a2, ..., an (1 ≤ ai ≤ M) which is original sequence.

输出解释
For each test contains 1 lines :
The line contains M integer, the i-th integer is the answer shows above when d is the i-th number.
输入样例 
3 3 3
3 3 3
3 5 3
1 2 3
输出样例 
7 1 0
59 3 0 1 1
提示
In the first test case :
when d = 1, {b} can be :
(1, 1, 1)
(1, 1, 2)
(1, 2, 1)
(1, 2, 2)
(2, 1, 1)
(2, 1, 2)
(2, 2, 1)
when d = 2, {b} can be :
(2, 2, 2)
And because {b} must have exactly K number(s) different from {a}, so {b} can't be (3, 3, 3), so Answer = 0
来自杭电HDUOJ的附加信息
Recommend zhuyuanchen520
该题目是Virtual Judge题目，来自 杭电HDUOJ
题目来源 2013 Multi-University Training Contest 7
源链接： HDU-4675
最后修改于 2020-10-25T23:15:42+00:00 由爬虫自动更新
共提交 0 次
通过率 --%
时间上限 内存上限
6000/3000MS(Java/Others) 65535/65535K(Java/Others)