CF1263C.Everyone is a Winner!
普及/提高-
通过率:0%
时间限制:1.00s
内存限制:256MB
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题目描述
On the well-known testing system MathForces, a draw of n rating units is arranged. The rating will be distributed according to the following algorithm: if k participants take part in this event, then the n rating is evenly distributed between them and rounded to the nearest lower integer, At the end of the drawing, an unused rating may remain — it is not given to any of the participants.
For example, if n=5 and k=3, then each participant will recieve an 1 rating unit, and also 2 rating units will remain unused. If n=5, and k=6, then none of the participants will increase their rating.
Vasya participates in this rating draw but does not have information on the total number of participants in this event. Therefore, he wants to know what different values of the rating increment are possible to get as a result of this draw and asks you for help.
For example, if n=5, then the answer is equal to the sequence 0,1,2,5. Each of the sequence values (and only them) can be obtained as ⌊n/k⌋ for some positive integer k (where ⌊x⌋ is the value of x rounded down): 0=⌊5/7⌋, 1=⌊5/5⌋, 2=⌊5/2⌋, 5=⌊5/1⌋.
Write a program that, for a given n, finds a sequence of all possible rating increments.
在著名的评测系统 MathForces 上,组织了一场总计 n 分的评分抽奖活动。评分将按如下规则分配:若共有 k 名参与者,则这 n 分将平均分配给所有参与者,并向下取整(即取不大于该值的最大整数)。抽奖结束后,可能剩余未分配的评分——这部分评分不会分配给任何参与者。
例如,若 n=5 且 k=3,则每名参与者获得 1 分,同时剩余 2 分未使用;若 n=5 且 k=6,则没有任何参与者能提升其评分。
瓦西亚参与了此次评分抽奖,但他并不知道本次活动的总参与人数。因此,他希望了解:通过此次抽奖,自己可能获得哪些不同的评分增量值?他请你帮忙解决这个问题。
例如,当 n=5 时,答案为序列 0,1,2,5。该序列中的每个值(且仅这些值)均可表示为 ⌊n/k⌋ 的形式(其中 ⌊x⌋ 表示对 x 向下取整),且 k 为某个正整数:0=⌊5/7⌋,1=⌊5/5⌋,2=⌊5/2⌋,5=⌊5/1⌋。
请编写一个程序,对于给定的 n,输出所有可能的评分增量值构成的序列。
输入格式
The first line contains integer number t (1≤t≤10) — the number of test cases in the input. Then t test cases follow.
Each line contains an integer n (1≤n≤109) — the total number of the rating units being drawn.
第一行包含一个整数 t(1≤t≤10)—— 输入中测试用例的数量。随后是 t 个测试用例。
每行包含一个整数 n(1≤n≤109)—— 待绘制的评分单位总数。
输出格式
Output the answers for each of t test cases. Each answer should be contained in two lines.
In the first line print a single integer m — the number of different rating increment values that Vasya can get.
In the following line print m integers in ascending order — the values of possible rating increments.
输出每个测试用例的答案。每个答案应包含两行。
第一行输出一个整数 m —— Vasya 可能得到的不同评分增量值的个数。
第二行按升序输出 m 个整数 —— 所有可能的评分增量值。
输入输出样例
输入#1
4 5 11 1 3
输出#1
4 0 1 2 5 6 0 1 2 3 5 11 2 0 1 3 0 1 3
输入解题思路,AI测评打分。不知道怎么写?