CC

题目链接

时空限制 1000ms / 128MB

Problem Description

题目背景

数学题，无背景

题目描述

给出正整数n和k，计算G(n, k)=k mod 1 + k mod 2 + k mod 3 + … + k mod n的值，其中k mod i表示k除以i的余数。例如G(10, 5)=5 mod 1 + 5 mod 2 + 5 mod 3 + 5 mod 4 + 5 mod 5 …… + 5 mod 10=0+1+2+1+0+5+5+5+5+5=29

题目链接

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)

Problem Description

There are many trees forming a m * n grid, the grid starts from (1,1). Farmer Sherlock is standing at (0,0) point. He wonders how many trees he can see. If two trees and Sherlock are in one line, Farmer Sherlock can only see the tree nearest to him.

题目链接

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 524288/524288 K (Java/Others)
Total Submission(s): 131 Accepted Submission(s): 41

Problem Description

There is a positive integer sequence a1,a2,…,an with some unknown positions, denoted by 0. >Little Q will replace each 0 by a random integer within the range [1,m] equiprobably. After that, he >will calculate the value of this sequence using the following formula :

题目链接

Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 524288/524288 K (Java/Others)

Total Submission(s): 446 Accepted Submission(s): 91

Problem Description

After trying hard for many years, Little Q has finally received an astronaut license. To celebrate the fact, he intends to buy himself a spaceship and make an interstellar travel.

Little Q knows the position of n planets in space, labeled by 1 to n. To his surprise, these planets are all coplanar. So to simplify, Little Q put these n planets on a plane coordinate system, and calculated the coordinate of each planet (xi,yi).

题目链接

题目

小TT最近学习了高斯消元法解方程组,现在他的问题来了，如果是以下的方程，那么应该如何解呢?

C(n1,m1)==0 (mod M)

C(n2,m2)==0 (mod M)

C(n3,m3)==0 (mod M)

…

题目链接

题目

Your task in this problem is to determine the number of divisors of Cnk. Just for fun – or do you need any special reason for such a useful computation?

Input

The input consists of several instances. Each instance consists of a single line containing two integers n and k (0 ≤ k ≤ n ≤ 431), separated by a single space.

题目链接

题目

Let {x} = 0.a1a2a3... be the binary representation of the fractional part of a rational number z. Suppose that {x} is periodic then, we can write

{x} = 0.a1a2...ar(ar+1ar+2...ar+s)w

for some integers r and s with r ≥ 0 and s > 0. Also, (ar+1ar+2...ar+s)wdenotes a nonterminating and repeating binary subsequence of {x}.

题目链接

题目

Two positive integers are said to be relatively prime to each other if the Great Common Divisor (GCD) is 1. For instance, 1, 3, 5, 7, 9...are all relatively prime to 2006.

Now your job is easy: for the given integer m, find the K-th element which is relatively prime to m when these elements are sorted in ascending order.

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题目

Bob has a not even coin, every time he tosses the coin, the probability that the coin’s front face up is $qp(qp≤12)\frac{q}{p}(\frac{q}{p} \le \frac{1}{2})​p​​q​​(​p​​q​​≤​2​​1​​).$
The question is, when Bob tosses the coin kkk times, what’s the probability that the frequency of the coin facing up is even number.
If the answer is $\frac{X}{Y}​$​​, because the answer could be extremely large, you only need to print $(X∗Y^{−1})mod(10^9+7)(X * Y^{-1}) \mod (10^9+7)(X∗Y​−1​​)mod(10​^9​​+7).$

题目链接

题目

We define a sequence F:

⋅ F0=0,F1=1;
⋅ Fn=Fn−1+Fn−2 (n≥2).

Give you an integer k, if a positive number n can be expressed by
n=Fa1+Fa2+...+Fak where 0≤a1≤a2≤⋯≤ak, this positive number is mjf−good. Otherwise, this positive number is mjf−bad.
Now, give you an integer k, you task is to find the minimal positive mjf−bad number.
The answer may be too large. Please print the answer modulo 998244353.