华中农业大学预赛 B Handing Out Candies 余数的和

Problem B: Handing Out Candies

Time Limit: 1 Sec  Memory Limit: 128 MB
Submit: 258  Solved: 19
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Description

    After the 40th ACM-ICPC, Diao Yang is thinking about finding a girlfriend because he feels very lonely when doing ACM all the time. But because of his philandering, he finally decided to find N girlfriends. To achieve his goal, he wanted to find one girlfriend every day for N days continue. That is to say, at the ith day, he will have i girlfriends exactly.

    In order to make his N girlfriends happy, he decided to buy M candies everyday for N days continue. Every day all of his girlfriends can get candies, and he will give each of them the same amount of candies and the amount will be as much as possible. Then if there are some candies left, he will eat them by himself.

    Now the problem is, Diao Yang want to know how many candies he can eat total by himself after N days continue.

Input

    The first line contains an integer T, indicating the total number of test cases. Each test case is a line with two integers N 15N" style="box-sizing: border-box; 9pt; height: 15.75pt;"> and M ( 151鈮?/m:t>N&lolt;231" style="box-sizing: border-box; 63.75pt; height: 15.75pt;">  ,  150鈮?/m:t>M&lolt;231" style="box-sizing: border-box; 65.25pt; height: 15.75pt;"> ).

Output

    For each test case, output the answer in one line.

Sample Input

2
5 7
6 4

Sample Output

7
9
　　　　N
题意：求∑  ( m%i);
　　　　i=1
思路：会发现M对一个数取模成等差数列；

#include<iostream>
#include<cstdio>
#include<cmath>
#include<string>
#include<queue>
#include<algorithm>
#include<stack>
#include<cstring>
#include<vector>
#include<list>
#include<set>
#include<map>
using namespace std;
#define ll long long
#define mod 1000000007
#define inf 999999999
#define esp 0.00000000001
//#pragma comment(linker, "/STACK:102400000,102400000")
int scan()
{
    int res = 0 , ch ;
    while( !( ( ch = getchar() ) >= '0' && ch <= '9' ) )
    {
        if( ch == EOF ) return 1 << 30 ;
    }
    res = ch - '0' ;
    while( ( ch = getchar() ) >= '0' && ch <= '9' )
        res = res * 10 + ( ch - '0' ) ;
    return res ;
}
int main()
{
    ll x,y,z,i,t;
    scanf("%lld",&x);
    while(x--)
    {
        scanf("%lld%lld",&y,&z);
        ll ans=max(y-z,0LL)*z;
        ll huan=min(y,z);
        for(i=2;i<=huan;i++)
        {
            if(z%i!=0)
            {
                ll d=z/i;
                ll maxx=min((z%i)/d+1,huan-i+1);
                d=-d;
                ans+=(z%i)*maxx+(maxx*(maxx-1)/2)*d;
                i+=maxx-1;
            }
        }
        printf("%lld
",ans);
    }
    return 0;
}