[POI 2007]ZAP-Queries

Description

Byteasar the Cryptographer works on breaking the code of BSA (Byteotian Security Agency). He has alreadyfound out that whilst deciphering a message he will have to answer multiple queries of the form"for givenintegers $a$, $b$ and $d$, find the number of integer pairs $(x,y)$ satisfying the following conditions:

$1le xle a$,$1le yle b$,$gcd(x,y)=d$, where $gcd(x,y)$ is the greatest common divisor of $x$ and $y$".

Byteasar would like to automate his work, so he has asked for your help.

TaskWrite a programme which:

reads from the standard input a list of queries, which the Byteasar has to give answer to, calculates answers to the queries, writes the outcome to the standard output.

FGD正在破解一段密码，他需要回答很多类似的问题：对于给定的整数a,b和d，有多少正整数对x,y，满足x<=a，y<=b，并且gcd(x,y)=d。作为FGD的同学，FGD希望得到你的帮助。

Input

The first line of the standard input contains one integer $n$ ($1le nle 50 000$),denoting the number of queries.

The following $n$ lines contain three integers each: $a$, $b$ and $d$($1le dle a,ble 50 000$), separated by single spaces.

Each triplet denotes a single query.

Output

Your programme should write $n$ lines to the standard output. The $i$'th line should contain a single integer: theanswer to the $i$'th query from the standard input.

Sample Input

2
4 5 2
6 4 3

Sample Output

3
2

题解

双倍经验。去掉容斥就好了，分析见超链接。

//It is made by Awson on 2018.1.21
#include <set>
#include <map>
#include <cmath>
#include <ctime>
#include <queue>
#include <stack>
#include <cstdio>
#include <string>
#include <vector>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#define LL long long
#define Abs(a) ((a) < 0 ? (-(a)) : (a))
#define Max(a, b) ((a) > (b) ? (a) : (b))
#define Min(a, b) ((a) < (b) ? (a) : (b))
#define Swap(a, b) ((a) ^= (b), (b) ^= (a), (a) ^= (b))
#define writeln(x) (write(x), putchar('
'))
#define lowbit(x) ((x)&(-(x)))
using namespace std;
const int N = 50000;
void read(int &x) {
    char ch; bool flag = 0;
    for (ch = getchar(); !isdigit(ch) && ((flag |= (ch == '-')) || 1); ch = getchar());
    for (x = 0; isdigit(ch); x = (x<<1)+(x<<3)+ch-48, ch = getchar());
    x *= 1-2*flag;
}
void write(LL x) {
    if (x > 9) write(x/10);
    putchar(x%10+48);
}

int a, b, k, mu[N+5];

void get_mu() {
    int isprime[N+5], prime[N+5], tot = 0;
    memset(isprime, 1, sizeof(isprime)); isprime[1] = 0, mu[1] = 1;
    for (int i = 2; i <= N; i++) {
    if (isprime[i]) mu[i] = -1, prime[++tot] = i;
    for (int j = 1; j <= tot && i*prime[j] <= N; j++) {
        isprime[i*prime[j]] = 0;
        if (i%prime[j]) mu[i*prime[j]] = -mu[i];
        else {mu[i*prime[j]] = 0; break; }
    }
    mu[i] += mu[i-1];
    }
}
LL cal(int a, int b) {
    if (a > b) Swap(a, b); LL ans = 0;
    for (int i = 1, last; i <= a; i = last+1) {
    last = Min(a/(a/i), b/(b/i));
    ans += (LL)(mu[last]-mu[i-1])*(a/i)*(b/i);
    }
    return ans;
}
void work() {
    read(a), read(b), read(k); writeln(cal(a/k, b/k));
}
int main() {
    int t; read(t); get_mu();
    while (t--) work();
    return 0;
}