hdu 5970 最大公约数

传送门：http://acm.hdu.edu.cn/showproblem.php?pid=5970

∑i=1n∑j=1m⌊(i∗j)f(i,j)⌋=∑j=1m∑i=1j∑k=0c−1∑l=0i+j∗(k+l∗c)<=n⌊(i+j∗(k+l∗c))c∗x∗x⌋=∑j=1m∑i=1j∑k=0c−1∑l=0i+j∗(k+l∗c)<=n⌊(i+j∗k)∗jc∗x∗x⌋+l∗j∗jx∗x

\sum_{i=1}^n \sum_{j=1}^m \lfloor \frac{(i*j)}{f(i,j)}\rfloor= \sum_{j=1}^m \sum_{i=1}^j \sum_{k=0}^{c-1} \sum_{l=0}^{i+j*(k+l*c)

//china no.1
#pragma comment(linker, "/STACK:1024000000,1024000000")
#include <vector>
#include <iostream>
#include <string>
#include <map>
#include <stack>
#include <cstring>
#include <queue>
#include <list>
#include <stdio.h>
#include <set>
#include <algorithm>
#include <cstdlib>
#include <cmath>
#include <iomanip>
#include <cctype>
#include <sstream>
#include <functional>
#include <stdlib.h>
#include <time.h>
#include <bitset>
using namespace std;#define pi acos(-1)
#define s_1(x) scanf("%d",&x)
#define s_2(x,y) scanf("%d%d",&x,&y)
#define s_3(x,y,z) scanf("%d%d%d",&x,&y,&z)
#define PI acos(-1)
#define endl '\n'
#define srand() srand(time(0));
#define me(x,y) memset(x,y,sizeof(x));
#define foreach(it,a) for(__typeof((a).begin()) it=(a).begin();it!=(a).end();it++)
#define close() ios::sync_with_stdio(0); cin.tie(0);
#define FOR(x,n,i) for(int i=x;i<=n;i++)
#define FOr(x,n,i) for(int i=x;i<n;i++)
#define fOR(n,x,i) for(int i=n;i>=x;i--)
#define fOr(n,x,i) for(int i=n;i>x;i--)
#define W while
#define sgn(x) ((x) < 0 ? -1 : (x) > 0)
#define bug printf("***********\n");
#define db double
#define ll long long
#define mp make_pair
#define pb push_back
typedef pair<long long int,long long int> ii;
typedef long long LL;
const int INF=0x3f3f3f3f;
const LL LINF=0x3f3f3f3f3f3f3f3fLL;
const int dx[]={-1,0,1,0,1,-1,-1,1};
const int dy[]={0,1,0,-1,-1,1,-1,1};
const int maxn=1e3+10;
const int maxx=600005;
const double EPS=1e-8;
const double eps=1e-8;
const int mod=1e9+7;
template<class T>inline T min(T a,T b,T c) { return min(min(a,b),c);}
template<class T>inline T max(T a,T b,T c) { return max(max(a,b),c);}
template<class T>inline T min(T a,T b,T c,T d) { return min(min(a,b),min(c,d));}
template<class T>inline T max(T a,T b,T c,T d) { return max(max(a,b),max(c,d));}
template <class T>
inline bool scan_d(T &ret){char c;int sgn;if (c = getchar(), c == EOF){return 0;}
while (c != '-' && (c < '0' || c > '9')){c = getchar();}sgn = (c == '-') ? -1 : 1;ret = (c == '-') ? 0 : (c - '0');
while (c = getchar(), c >= '0' && c <= '9'){ret = ret * 10 + (c - '0');}ret *= sgn;return 1;}inline bool scan_lf(double &num){char in;double Dec=0.1;bool IsN=false,IsD=false;in=getchar();if(in==EOF) return false;
while(in!='-'&&in!='.'&&(in<'0'||in>'9'))in=getchar();if(in=='-'){IsN=true;num=0;}else if(in=='.'){IsD=true;num=0;}
else num=in-'0';if(!IsD){while(in=getchar(),in>='0'&&in<='9'){num*=10;num+=in-'0';}}
if(in!='.'){if(IsN) num=-num;return true;}else{while(in=getchar(),in>='0'&&in<='9'){num+=Dec*(in-'0');Dec*=0.1;}}
if(IsN) num=-num;return true;}void Out(LL a){if(a < 0) { putchar('-'); a = -a; }if(a >= 10) Out(a / 10);putchar(a % 10 + '0');}
void print(LL a){ Out(a),puts("");}
//freopen( "in.txt" , "r" , stdin );
//freopen( "data.txt" , "w" , stdout );
//cerr << "run time is " << clock() << endl;//http://www.cnblogs.com/phile/p/6391465.html
LL n,m,p;
LL Fc[maxn][maxn];
LL Fcx[maxn][maxn];void f(LL x,LL y)
{LL tx=x,ty=y;LL c=0;while(y>0){c+=1;LL t=x%y;x=y;y=t;}Fc[tx][ty]=c;Fcx[tx][ty]=c*x*x;}void init()
{for(LL j=1; j<=666; j++){for(LL i=0; i<=j; i++){f(i,j);}}
}
void solve()
{scanf("%I64d%I64d%I64d",&n,&m,&p);LL ans=0;FOR(1,m,j){for(int i=1;i<=j&&i<=n;i++){for(int k=0;k<Fc[i][j];k++){if(i+k*j>n) break;LL b=(i+j*k)*j/Fcx[i][j];LL d=Fc[i][j]*j*j/Fcx[i][j];LL t=(n-(i+j*k))/(Fc[i][j]*j)+1;//倍数ans=(ans+b*t%p+(t-1)*t/2%p*d%p)%p;}}}print(ans);
}int main()
{init();int t;scan_d(t);W(t--){solve();}
}

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