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Codeforces 题库 101-200

Codeforces

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CODEFORCES PROBLEMSET

#101-#200

2013-4-11

Sorted by Jerry Xu in Shanghai

Codeforces is a Russian website dedicated to competitive programming. It was created and

is currently maintained by group of sportsmen from Saratov State University led by Mikhail

Mirzayanov.

Codeforces provides to all users following main services:

Participation in the short (2-hours) contests, so-called "Codeforces Rounds", held about

once a week;

Ability to solve problems from previous contests for training purposes;

"Polygon" for creating and testing problems;

Kind of social-networking by using of internal public blogs.

Contestants are rated by system similar to ELO. There are usually no prizes for winners,

though 100 winners of 100-th Codeforces Round received a T-Shirt. Some bigger contests

(mostly country internal) are hosted on Codeforces base, among them "Yandex Algorithm

2011", provided by Yandex - one of biggest Russian IT-companies.

Website: Codeforces.com

101A. Homework

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Once when Gerald studied in the first year at school, his teacher gave the class the

following homework. She offered the students a string consisting of n small Latin

letters; the task was to learn the way the letters that the string contains are written.

However, as Gerald is too lazy, he has no desire whatsoever to learn those letters.

That's why he decided to lose some part of the string (not necessarily a connected

part). The lost part can consist of any number of segments of any length, at any

distance from each other. However, Gerald knows that if he loses more than k

characters, it will be very suspicious.

Find the least number of distinct characters that can remain in the string after no

more than k characters are deleted. You also have to find any possible way to

delete the characters.

Input

The first input data line contains a string whose length is equal to n (1 ≤ n ≤ 10

The string consists of lowercase Latin letters. The second line contains the number

k (0 ≤ k ≤ 10

Output

Print on the first line the only number m — the least possible number of different

characters that could remain in the given string after it loses no more than k

characters.

Print on the second line the string that Gerald can get after some characters are

lost. The string should have exactly m distinct characters. The final string should be

the subsequence of the initial string. If Gerald can get several different strings with

exactly m distinct characters, print any of them.

Sample test(s)

Input

aaaaa

Output

aaaaa

Input

abacaba

Output

aaaa

Input

abcdefgh

Output

Note

In the first sample the string consists of five identical letters but you are only allowed

to delete 4 of them so that there was at least one letter left. Thus, the right answer is

1 and any string consisting of characters "a" from 1 to 5 in length.

In the second sample you are allowed to delete 4 characters. You cannot delete all

the characters, because the string has length equal to 7. However, you can delete

all characters apart from "a" (as they are no more than four), which will result in the

"aaaa" string.

In the third sample you are given a line whose length is equal to 8, and k = 10, so

that the whole line can be deleted. The correct answer is 0 and an empty string.

101B. Buses

time limit per test

2 seconds

memory limit per test

265 megabytes

input

standard input

output

standard output

Little boy Gerald studies at school which is quite far from his house. That's why he

has to go there by bus every day. The way from home to school is represented by a

segment of a straight line; the segment contains exactly n + 1 bus stops. All of them

are numbered with integers from 0 to n in the order in which they follow from

Gerald's home. The bus stop by Gerald's home has number 0 and the bus stop by

the school has number n.

There are m buses running between the house and the school: the i-th bus goes

from stop s

to t

< t

), visiting all the intermediate stops in the order in which they

follow on the segment. Besides, Gerald's no idiot and he wouldn't get off the bus

until it is still possible to ride on it closer to the school (obviously, getting off would

be completely pointless). In other words, Gerald can get on the i-th bus on any stop

numbered from s

to t

- 1 inclusive, but he can get off the i-th bus only on the bus

stop t

Gerald can't walk between the bus stops and he also can't move in the direction

from the school to the house.

Gerald wants to know how many ways he has to get from home to school. Tell him

this number. Two ways are considered different if Gerald crosses some segment

between the stops on different buses. As the number of ways can be too much, find

the remainder of a division of this number by 1000000007 (10

+ 7).

Input

The first line contains two space-separated integers: n and m

(1 ≤ n ≤ 10

, 0 ≤ m ≤ 10

). Then follow m lines each containing two integers s

, t

They are the numbers of starting stops and end stops of the buses (0 ≤ s

< t

≤ n).

Output

Print the only number — the number of ways to get to the school modulo

1000000007 (10

+ 7).

Sample test(s)

Input

2 2

0 1

1 2

Output

Input

3 2

0 1

1 2

Output

Input

5 5

0 1

0 2

0 3

0 4

0 5

Output

Note

The first test has the only variant to get to school: first on bus number one to the bus

stop number one; then on bus number two to the bus stop number two.

In the second test no bus goes to the third bus stop, where the school is positioned.

Thus, the correct answer is 0.

In the third test Gerald can either get or not on any of the first four buses to get

closer to the school. Thus, the correct answer is 2

= 16.

101C. Vectors

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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2014-04-08

题目比较难，不过还是很有价值和意义的

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