HDU4611+数学

/*
找规律
题意：abs(i%A - i%B) 对i从0~N-1求和
从0~N-1一个一个算必TLE，着A，B两者差相同的部分合并起来算
*/
#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<algorithm>
#include<iostream>
#include<queue>
#include<map>
#include<math.h>
using namespace std;
typedef long long int64;
//typedef __int64 int64;
const int maxn = 105;
const int inf = 0x7fffffff;
const double pi=acos(-1.0);
const double eps = 1e-8;

int64 gcd( int64 a,int64 b ){
    int64 r;
    while( b ){
        r = a%b;
        a = b;
        b = r;
    }
    return a;
}

int64 lcm( int64 a,int64 b,int64 Gcd ){
    return a*b/Gcd;
}

int64 Abs( int64 a ){
    if( a<0 ) return -a;
    else return a;
}

int64 solve( int64 n,int64 a,int64 b ){
    int64 Index,tmpLen,res,Indexa,Indexb;
    res = Index = Indexa = Indexb = 0;
    while( Index<n ){
        tmpLen = min( a-Indexa,b-Indexb );
        if( Index+tmpLen>n ) tmpLen = n-Index;//Index:表示新的开始分割的位置
        res += tmpLen*Abs( Indexa-Indexb );
        Indexa += tmpLen, Indexa %= a;
        Indexb += tmpLen, Indexb %= b;
        Index += tmpLen;
    }
    return res;    
}        

int main(){
    int T;
    scanf("%d",&T);
    while( T-- ){
        int64 n,a,b;
        //scanf("%lld%lld%lld",&n,&a,&b);
        scanf("%I64d%I64d%I64d",&n,&a,&b);
        int64 LCM = lcm( a,b,gcd(a,b) );
        int64 ans = 0;
        if( LCM>=n ) ans = solve( n,a,b );
        else ans = (n/LCM)*solve( LCM,a,b )+solve( n%LCM,a,b );
        //printf("%lld\n",ans);
        printf("%I64d\n",ans);
    }
    return 0;
}