# CQU Qualification Solution

UPD1: 还有3题没补完明天早上补qwq

### A.取石子游戏

#### Description

1堆石子有n个,两人轮流取.先取者第1次可以取任意多个，但不能全部取完.以后每次取的石子数不能超过上次取子数的2倍。取完者胜.先取者负输出"Second win".先取者胜输出"First win".

### C.Bob's Race

#### Description

Bob wants to hold a race to encourage people to do sports. He has got trouble in choosing the route. There are N houses and N - 1 roads in his village. Each road connects two houses, and all houses are connected together. To make the race more interesting, he requires that every participant must start from a different house and run AS FAR AS POSSIBLE without passing a road more than once. The distance difference between the one who runs the longest distance and the one who runs the shortest distance is called “race difference” by Bob. Bob does not want the “race difference”to be more than Q. The houses are numbered from 1 to N. Bob wants that the No. of all starting house must be consecutive. He is now asking you for help. He wants to know the maximum number of starting houses he can choose, by other words, the maximum number of people who can take part in his race.

#### Input

There are several test cases.
The first line of each test case contains two integers N and M. N is the number of houses, M is the number of queries.
The following N-1 lines, each contains three integers, x, y and z, indicating that there is a road of length z connecting house x and house y.
The following M lines are the queries. Each line contains an integer Q, asking that at most how many people can take part in Bob’s race according to the above mentioned rules and under the condition that the“race difference”is no more than Q.The input ends with N = 0 and M = 0.

(N<=50000 M<=500 1<=x,y<=N 0<=z<=5000 Q<=10000000)

#### Output

For each test case, you should output the answer in a line for each query.

orz会双端单调队列的鸟神

### D - Intersection

#### Description

You are given two set of points. The first set is determined by the equation A1x + B1y + C1 = 0, and the second one is determined by the equation A2x + B2y + C2 = 0.

Write the program which finds the number of points in the intersection of two given sets.

#### Input

The first line of the input contains three integer numbers A1, B1, C1 separated by space. The second line contains three integer numbersA2, B2, C2 separated by space. All the numbers are between -100 and 100, inclusive.

#### Output

Print the number of points in the intersection or -1 if there are infinite number of points.

#### Solution

1. 空集
2. 无限集
3. 交集为$1$

### G - Subway Innovation

#### Description

Berland is going through tough times — the dirt price has dropped and that is a blow to the country's economy. Everybody knows that Berland is the top world dirt exporter!

The President of Berland was forced to leave only k of the currently existing n subway stations.

The subway stations are located on a straight line one after another, the trains consecutively visit the stations as they move. You can assume that the stations are on the Ox axis, the i-th station is at point with coordinate xi. In such case the distance between stations i andj is calculated by a simple formula |xi - xj|.

Currently, the Ministry of Transport is choosing which stations to close and which ones to leave. Obviously, the residents of the capital won't be too enthusiastic about the innovation, so it was decided to show the best side to the people. The Ministry of Transport wants to choose such k stations that minimize the average commute time in the subway!

Assuming that the train speed is constant (it is a fixed value), the average commute time in the subway is calculated as the sum of pairwise distances between stations, divided by the number of pairs (that is ) and divided by the speed of the train.

Help the Minister of Transport to solve this difficult problem. Write a program that, given the location of the stations selects such kstations that the average commute time in the subway is minimized.

#### Input

The first line of the input contains integer n (3 ≤ n ≤ 3·105) — the number of the stations before the innovation. The second line contains the coordinates of the stations x1, x2, ..., xn ( - 108 ≤ xi ≤ 108). The third line contains integer k (2 ≤ k ≤ n - 1) — the number of stations after the innovation.

The station coordinates are distinct and not necessarily sorted.

#### Output

Print a sequence of k distinct integers t1, t2, ..., tk (1 ≤ tj ≤ n) — the numbers of the stations that should be left after the innovation in arbitrary order. Assume that the stations are numbered 1 through n in the order they are given in the input. The number of stations you print must have the minimum possible average commute time among all possible ways to choose k stations. If there are multiple such ways, you are allowed to print any of them.

#### Solution

$\sum$里的内容可以用前缀和预处理出来

### I - Kefa and Park

#### Description

Kefa decided to celebrate his first big salary by going to the restaurant.

He lives by an unusual park. The park is a rooted tree consisting of n vertices with the root at vertex 1. Vertex 1 also contains Kefa's house. Unfortunaely for our hero, the park also contains cats. Kefa has already found out what are the vertices with cats in them.

The leaf vertices of the park contain restaurants. Kefa wants to choose a restaurant where he will go, but unfortunately he is very afraid of cats, so there is no way he will go to the restaurant if the path from the restaurant to his house contains more than mconsecutivevertices with cats.

Your task is to help Kefa count the number of restaurants where he can go.

#### Input

The first line contains two integers, n and m (2 ≤ n ≤ 105, 1 ≤ m ≤ n) — the number of vertices of the tree and the maximum number of consecutive vertices with cats that is still ok for Kefa.

The second line contains n integers a1, a2, ..., an, where each ai either equals to 0 (then vertex i has no cat), or equals to 1 (then vertex i has a cat).

Next n - 1 lines contains the edges of the tree in the format "xiyi" (without the quotes) (1 ≤ xi, yi ≤ n, xi ≠ yi), where xi and yi are the vertices of the tree, connected by an edge.

It is guaranteed that the given set of edges specifies a tree.

#### Output

A single integer — the number of distinct leaves of a tree the path to which from Kefa's home contains at most m consecutive vertices with cats.

### J - Amr and The Large Array

#### Description

Amr has got a large array of size n. Amr doesn't like large arrays so he intends to make it smaller.

Amr doesn't care about anything in the array except the beauty of it. The beauty of the array is defined to be the maximum number of times that some number occurs in this array. He wants to choose the smallest subsegment of this array such that the beauty of it will be the same as the original array.

Help Amr by choosing the smallest subsegment possible.

#### Input

The first line contains one number n (1 ≤ n ≤ 105), the size of the array.

The second line contains n integers ai (1 ≤ ai ≤ 106), representing elements of the array.

#### Output

Output two integers l, r (1 ≤ l ≤ r ≤ n), the beginning and the end of the subsegment chosen respectively.

If there are several possible answers you may output any of them.