Problem D. Database ≡

Statement

Peter studies the theory of relational databases. Table in the relational database consists of values that are arranged in rows and columns.

There are different normal forms that database may adhere to. Normal forms are designed to minimize the redundancy of data in the database. For example, a database table for a library might have a row for each book and columns for book name, book author, and author's email.

If the same author wrote several books, then this representation is clearly redundant. To formally define this kind of redundancy Peter has introduced his own normal form. A table is in Peter's Normal Form (PNF) if and only if there is no pair of rows and a pair of columns such that the values in the corresponding columns are the same for both rows.

The first table is clearly not in PNF, since values for 2rd and 3rd columns repeat in 2nd and 3rd rows. However, if we introduce unique author identifier and split this table into two tables — one containing book name and author id, and the other containing book id, author name, and author email, then both resulting tables will be in PNF.

Given a table your task is to figure out whether it is in PNF or not.

Input file format

The first line of the input file contains two integer numbers n and m (1 ≤ n ≤ 10 000, 1 ≤ m ≤ 10), the number of rows and columns in the table. The following n lines contain table rows. Each row has m column values separated by commas. Column values consist of ASCII characters from space (ASCII code 32) to tilde (ASCII code 126) with the exception of comma (ASCII code 44). Values are not empty and have no leading and trailing spaces. Each row has at most 80 characters (including separating commas).

Output file format

If the table is in PNF write to the output file a single word "YES" (without quotes). If the table is not in PNF, then write three lines. On the first line write a single word "NO" (without quotes). On the second line write two integer row numbers r₁ and r₂ (1 ≤ r₁, r₂ ≤ n, r₁ ≠ r₂), on the third line write two integer column numbers c₁ and c₂ (1 ≤ c₁, c₂ ≤ m, c₁ ≠ c₂), so that values in columns c₁ and c₂ are the same in rows r₁ and r₂.

Sample tests

3 3
How to compete in ACM ICPC,Peter,peter@neerc.ifmo.ru
How to win ACM ICPC,Michael,michael@neerc.ifmo.ru
Notes from ACM ICPC champion,Michael,michael@neerc.ifmo.ru

NO
2 3
2 3

2 3
1,Peter,peter@neerc.ifmo.ru
2,Michael,michael@neerc.ifmo.ru

YES

Problem F. Funny Language ≡

Statement

There is a well know game with words. Given a word you have to write as many other words as possible using the letters from the given word. If the letter repeats multiple times in the original word, you can use it up to as many times in the new words. The order of letters in the original word does not matter. For example, given the word CONTEST you can write NOTE, NET, ON, TEST, SET, etc.

Now you are in charge of writing a new dictionary. Your task is to sneak n new words into it. You know in advance m words W_i (1 ≤ i ≤ m) that you will have to play a game with and you need to figure out which new n words to add to the dictionary to maximize the total number of words you can write out of these m words.

More formally, find such a set of nonempty words S where |S| = n, W_i ∉ S for any i, and ∑_{1 ≤ i ≤ m}|S_i| is maximal, where S_i ⊂ S is the set of words that can be written using letters from W_i.

Input file format

The first line of the input file contains two integer numbers n (1 ≤ n ≤ 100) — the number of new words you can add to the dictionary and m (1 ≤ m ≤ 1 000) — the number of words you will play the game with. The following m lines contain original words. Each word consists of at most 100 uppercase letters from A to Z.

Output file format

Write to the output file n lines with a new word on a line.

Sample tests

3 5
A
ACM
ICPC
CONTEST
NEERC

C
CN
E

Problem J. Java Certification ≡

Statement

You have just completed Java Certification exam that contained n questions. You have a score card that explains your performance. The example of the scorecard is given below.

From this scorecard you can infer that the questions are broken down into m categories (in the above example m = 6). Each category contains n_i questions (1 ≤ n_i ≤ n), so that ∑_{1 ≤ i ≤ m} n_i = n. You know that you have correctly answered k questions out of n (in the above example k = 78 and n = 87), so you can easily find the number of incorrect answers w = n − k (in the above example w = 9).

You do remember several questions that you were unsure about and you can guess what category they belong to. To figure out if your answers on those questions were right or wrong, you really want to know how many incorrect answers you have given in each category.

Let w_i (0 ≤ w_i ≤ n_i) be the number of incorrect answers in i-th category, ∑_{1 ≤ i ≤ m} w_i = w. From the scorecard you know the percentage of correct answers in each category. That is, for each i from 1 to m you know the value of 100(n_i − w_i) / n_i rounded to the nearest integer. The value with a fractional part of 0.5 is rounded to the nearest even integer.

It may not be possible to uniquely find the valid values for w_i. However, you guess that the questions are broken down into categories in a mostly uniform manner. You have to find the valid values of w_i and n_i, so that to minimize the difference between the maximum value of n_i and the minimum value of n_i. If there are still multiple possible values for w_i and n_i, then find any of them.

Input file format

The first line of the input file contains three integer numbers — k, n, and m, where k (0 ≤ k ≤ n) is the number of correctly answered questions, n (1 ≤ n ≤ 100) is the total number of questions, m (1 ≤ m ≤ 10) is the number of question categories. The following m lines of the input file contain one integer number from 0 to 100 (inclusive) on a line — percentages of the number of the correct answers in each category. The input file always corresponds to some valid set of w_i and n_i.

Output file format

Write to the output file m lines with two integer numbers w_i and n_i on a line, separated by a space — the number of incorrect answers and the total number of questions in each category, satisfying constraints as given in the problem statement.

Sample tests

78 87 6
100
100
83
92
75
93

0 13
0 13
3 18
1 13
4 16
1 14