【ZOJ - 2116】Christopher's Christmas Letter(Lucas)

Dashing thro’ the snow,
In a one-horse open sleigh,
O’er the fields we go,
Laughing all the way;
Bells on bobtail ring,
Making spirits bright;
What fun it is to ride and sing
A sleighing song tonight!
Jingle, bells! Jingle, bells!
Jingle all the way!
Oh! What fun it is to ride in a one-horse open sleigh!

The Christmas Eve last year becomes a story that filled Christopher’s hearts with joy. With your help on “Souvenirs of Love” problem, Christopher has already been out of danger. (If you’re interested in the background, please see Christopher’s Key Ring)

This time, Christopher received a letter from Father Christmas. It was sent on Christmas Eve, but coz the mailing jam, it was just received. To his surprise, Father Christmas didn’t fall asleep as well as Christopher (but different reason ;). What is Santa Claus’s trouble? Let’s see, it’s a math problem:

There’re N different XX toys, to be sent to city X. Each time Santa Claus will send M (0 <= M <= N) toys to a single person as presents. The number of ways for fixed M is well-known I think. It is very strange that the people in city X hate such number M for a fixed N, if and only if the number of ways for it is multiple of a fixed prime P.

Santa Claus wonders how many Ms will be satisfying (not be hated by people in city X).

Input

The first line of the input contains one integer X (1 <= X <= 500), which is the number of test cases.

Next X lines each contains two integers N (1 <= N <= 10^100) and P (a prime, 2 <= P <= 10^7).

Output

You should write exactly X lines to the output. Each line contains the total number of satisfying Ms for that test case.

Sample Input

2
6 7
6 2

Sample Output

0
3

(adviser)
Site: http://zhuzeyuan.hp.infoseek.co.jp/index.files/our_contest_20040619.htm

问题问得就是m在0到n有多少个m使得Cmn% p≡0Cnm%p≡0C_n^m\%\ p\equiv0

这个只要一些Luas定理一个性质。
我们把n和m都按p进制表示：

n=n0+n1p+n2p2+...+nkpkm=m0+m1p+m2p2+...+mkpkn=n0+n1p+n2p2+...+nkpkm=m0+m1p+m2p2+...+mkpk

n=n_0+n_1p+n_2p^2+...+n_kp^k\\m=m_0+m_1p+m_2p^2+...+m_kp^k
那么

Cmn% p≡∏i=0kCmini% pCnm%p≡∏i=0kCnimi%p

C_n^m\%\ p\equiv\prod_{i=0}^kC_{n_i}^{m_i}\%\ p

若存在任意一项ni<mini<min_i,则这个组合数与0同余。
所以我们可以反过来看使得这个组合数不为0的时候m的情况，那么就是∏ki=0(ni+1)∏i=0k(ni+1)\prod_{i=0}^k(n_i+1)
答案就是n+1减掉这个不合法的。

java大数写的爽啊。
代码：

import java.math.BigInteger;
import java.util.Scanner;public class Main
{public static void main(String[] args){Scanner sc=new Scanner(System.in);int t=sc.nextInt();while((t--)>0){BigInteger n=sc.nextBigInteger();BigInteger p=sc.nextBigInteger();int cnt=0;BigInteger ans=n;BigInteger temp=BigInteger.ONE;while(!n.equals(BigInteger.ZERO)){temp=temp.multiply(n.mod(p).add(BigInteger.ONE));n=n.divide(p);}System.out.println(ans.subtract(temp).add(BigInteger.ONE));}}}

【ZOJ - 2116】Christopher's Christmas Letter(Lucas)相关推荐

【zoj 3547】【zoj 3548】8.17模拟赛
题目来源:未知,zoj3547,3548 t1 [问题描述] 若干年之后,XJH找工作面试,面试官给了他这样一个题目. 你有一个N*N的回型矩阵,保证N是奇数. 例如,当N=5的时候,矩阵如下: 现在 ...
【ZOJ 4062】Plants vs. Zombies
[链接] 我是链接,点我呀:) [题意] [题解] 二分最后的最大抵御值mid. 然后对于每个蘑菇. 都能算出来它要浇水几次mid/ai 然后如果第i个蘑菇没浇水达到要求次数. 就在i和i+1之间来回 ...
【POJ - 1789】【ZOJ - 2158】【SCU - 1832】Truck History （最小生成树）
题干: Description Advanced Cargo Movement, Ltd. uses trucks of different types. Some trucks are used f ...
【ZOJ 2974】Just Pour the Water(矩阵快速幂)
传送门:http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemCode=2974 题意给出n个杯子与初始水量同时进行操作将其中的水同时平均 ...
【ZOJ - 3329】One Person Game（带循环的概率dp，数学期望，高斯消元，数学）
题干: There is a very simple and interesting one-person game. You have 3 dice, namely Die1, Die2 and D ...
【ZOJ - 2968 】Difference Game （贪心，思维模拟）
题干: Now you are going to play an interesting game. In this game, you are given two groups of distinc ...
*【ZOJ - 3703】Happy Programming Contest（带优先级的01背包）
题干: In Zhejiang University Programming Contest, a team is called "couple team" if it consi ...
【ZOJ - 4033】CONTINUE...? （思维，整体思想，分组思想）
题干: DreamGrid has classmates numbered from to . Some of them are boys and the others are girls. Ea ...
【ZOJ - 4032】Magic Points （思维，几何，构造）
题干: 解题报告: 想到了,这样绕圈构造.但是这样有个问题,最后一个点如何构造. 刚开始想的是n=奇数 , 就8 10 这样的连一条,n=偶数就8 11 这样的连一条,随便构造一下就行,但是发 ...

【ZOJ - 2116】Christopher's Christmas Letter(Lucas)

【ZOJ - 2116】Christopher's Christmas Letter(Lucas)相关推荐

最新文章

热门文章