CodeForces - 546D Soldier and Number Game

最新推荐文章于 2020-03-16 11:43:13 发布

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本文介绍了一个关于两个士兵进行的游戏，游戏的目标是通过不断除以质数的方式将初始值a!/b!减少至1，计算此过程中的最大可能轮数。文章提供了完整的解题思路与C++代码实现，利用预处理的方法高效地解决了问题。

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Soldier and Number Game

Two soldiers are playing a game. At the beginning first of them chooses a positive integer n and gives it to the second soldier. Then the second one tries to make maximum possible number of rounds. Each round consists of choosing a positive integer x > 1, such that n is divisible by x and replacing n with n / x. When nbecomes equal to 1 and there is no more possible valid moves the game is over and the score of the second soldier is equal to the number of rounds he performed.

To make the game more interesting, first soldier chooses n of form a! / b! for some positive integer a and b (a ≥ b). Here by k! we denote the factorial of k that is defined as a product of all positive integers not large than k.

What is the maximum possible score of the second soldier?

Input

First line of input consists of single integer t (1 ≤ t ≤ 1 000 000) denoting number of games soldiers play.

Then follow t lines, each contains pair of integers a and b (1 ≤ b ≤ a ≤ 5 000 000) defining the value of n for a game.

Output

For each game output a maximum score that the second soldier can get.

Examples

Input

2
3 1
6 3

Output

2
5

题目大意：

给出一个n，n开始是a!/b!，每次用一个x去整除n得到新的n，
最后当n变成1的时候经过了几轮得分就是这个轮数，要求最大的分数是多少

思路：

就是求质因子的个数的问题。

a!/b!会约掉一部分,所以只要求出a~b+1的质因子数的和就行了，打个表记录一下1到5000000的质因子个数和

代码：

#include<stdio.h>
#include<string.h>
#include<algorithm>
#define N  5000010
using namespace std;
long long n,m,a[N];
void init()
{
    a[1]=a[2]=0;
    for(int i=2; i<N; ++i) //打表计算质因子的个数
    {
        if(!a[i])
        {
            for(int j=i; j<N; j+=i)
            {
                a[j]=a[j/i]+1;
            }
        }
    }
    for(int i=2; i<N; ++i)  //求前i的和
       a[i]=a[i]+a[i-1];
}
int main()
{
    init();
    int t;scanf("%d",&t);
    while(t--)
    {
        scanf("%d %d",&n,&m);
        printf("%lld\n",a[n]-a[m]);
    }
    return 0;
}