CF基础数学题
CF基础数学题
B. Divisors of Two Integers
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
Recently you have received two positive integer numbers x
and y. You forgot them, but you remembered a shuffled list containing all divisors of x (including 1 and x) and all divisors of y (including 1 and y). If d is a divisor of both numbers x and y at the same time, there are two occurrences of d
in the list.
For example, if x=4
and y=6 then the given list can be any permutation of the list [1,2,4,1,2,3,6]. Some of the possible lists are: [1,1,2,4,6,3,2], [4,6,1,1,2,3,2] or [1,6,3,2,4,1,2]
.
Your problem is to restore suitable positive integer numbers x
and y
that would yield the same list of divisors (possibly in different order).
It is guaranteed that the answer exists, i.e. the given list of divisors corresponds to some positive integers x
and y
.
Input
The first line contains one integer n
(2≤n≤128) — the number of divisors of x and y
.
The second line of the input contains n
integers d1,d2,…,dn (1≤di≤104), where di is either divisor of x or divisor of y. If a number is divisor of both numbers x and y
then there are two copies of this number in the list.
Output
Print two positive integer numbers x
and y
— such numbers that merged list of their divisors is the permutation of the given list of integers. It is guaranteed that the answer exists.
Example
Input
Copy
10
10 2 8 1 2 4 1 20 4 5
Output
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20 8
找出最大的那个数（所求的一个数），遍历把他的因子去掉那么剩下来的最大的数就是所求的另一个数。
#includeA. Ksusha and Array
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Ksusha is a beginner coder. Today she starts studying arrays. She has array a1, a2, …, an, consisting of n positive integers.
Her university teacher gave her a task. Find such number in the array, that all array elements are divisible by it. Help her and find the number!
Input
The first line contains integer n (1 ≤ n ≤ 105), showing how many numbers the array has. The next line contains integers a1, a2, …, an (1 ≤ ai ≤ 109) — the array elements.
Output
Print a single integer — the number from the array, such that all array elements are divisible by it. If such number doesn’t exist, print -1.
If there are multiple answers, you are allowed to print any of them.
Examples
Input
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3
2 2 4
Output
Copy
2
Input
Copy
5
2 1 3 1 6
Output
Copy
1
Input
Copy
3
2 3 5
Output
Copy
-1
#includeB. Square Difference
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Alice has a lovely piece of cloth. It has the shape of a square with a side of length a
centimeters. Bob also wants such piece of cloth. He would prefer a square with a side of length b centimeters (where b#include似乎时间复杂度更小的方法（适用对于范围在int内的数）
#include水
A. I’m bored with life
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
Holidays have finished. Thanks to the help of the hacker Leha, Noora managed to enter the university of her dreams which is located in a town Pavlopolis. It’s well known that universities provide students with dormitory for the period of university studies. Consequently Noora had to leave Vičkopolis and move to Pavlopolis. Thus Leha was left completely alone in a quiet town Vičkopolis. He almost even fell into a depression from boredom!
Leha came up with a task for himself to relax a little. He chooses two integers A and B and then calculates the greatest common divisor of integers “A factorial” and “B factorial”. Formally the hacker wants to find out GCD(A!, B!). It’s well known that the factorial of an integer x is a product of all positive integers less than or equal to x. Thus x! = 1·2·3·…·(x - 1)·x. For example 4! = 1·2·3·4 = 24. Recall that GCD(x, y) is the largest positive integer q that divides (without a remainder) both x and y.
Leha has learned how to solve this task very effective. You are able to cope with it not worse, aren’t you?
Input
The first and single line contains two integers A and B (1 ≤ A, B ≤ 109, min(A, B) ≤ 12).
Output
Print a single integer denoting the greatest common divisor of integers A! and B!.
Example
Input
Copy
4 3
Output
Copy
6
Note
Consider the sample.
4! = 1·2·3·4 = 24. 3! = 1·2·3 = 6. The greatest common divisor of integers 24 and 6 is exactly 6.
#include组合数
C. The World is a Theatre
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
There are n boys and m girls attending a theatre club. To set a play “The Big Bang Theory”, they need to choose a group containing exactly t actors containing no less than 4 boys and no less than one girl. How many ways are there to choose a group? Of course, the variants that only differ in the composition of the troupe are considered different.
Perform all calculations in the 64-bit type: long long for С/С++, int64 for Delphi and long for Java.
Input
The only line of the input data contains three integers n, m, t (4 ≤ n ≤ 30, 1 ≤ m ≤ 30, 5 ≤ t ≤ n + m).
Output
Find the required number of ways.
Please do not use the %lld specificator to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specificator.
Examples
Input
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5 2 5
Output
Copy
10
Input
Copy
4 3 5
Output
Copy
3
#includeB. Proper Nutrition
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
Vasya has n burles. One bottle of Ber-Cola costs a burles and one Bars bar costs b burles. He can buy any non-negative integer number of bottles of Ber-Cola and any non-negative integer number of Bars bars.
Find out if it’s possible to buy some amount of bottles of Ber-Cola and Bars bars and spend exactly n burles.
In other words, you should find two non-negative integers x and y such that Vasya can buy x bottles of Ber-Cola and y Bars bars and x·a + y·b = n or tell that it’s impossible.
Input
First line contains single integer n (1 ≤ n ≤ 10 000 000) — amount of money, that Vasya has.
Second line contains single integer a (1 ≤ a ≤ 10 000 000) — cost of one bottle of Ber-Cola.
Third line contains single integer b (1 ≤ b ≤ 10 000 000) — cost of one Bars bar.
Output
If Vasya can’t buy Bars and Ber-Cola in such a way to spend exactly n burles print «NO» (without quotes).
Otherwise in first line print «YES» (without quotes). In second line print two non-negative integers x and y — number of bottles of Ber-Cola and number of Bars bars Vasya should buy in order to spend exactly n burles, i.e. x·a + y·b = n. If there are multiple answers print any of them.
Any of numbers x and y can be equal 0.
Examples
Input
Copy
7
2
3
Output
Copy
YES
2 1
Input
Copy
100
25
10
Output
Copy
YES
0 10
Input
Copy
15
4
8
Output
Copy
NO
Input
Copy
9960594
2551
2557
Output
Copy
YES
1951 1949
Note
In first example Vasya can buy two bottles of Ber-Cola and one Bars bar. He will spend exactly 2·2 + 1·3 = 7 burles.
In second example Vasya can spend exactly n burles multiple ways:
buy two bottles of Ber-Cola and five Bars bars;
buy four bottles of Ber-Cola and don't buy Bars bars;
don't buy Ber-Cola and buy 10 Bars bars.
In third example it’s impossible to but Ber-Cola and Bars bars in order to spend exactly n burles.
水题
#include