模板 - 皮克定理

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;

struct Point;
typedef Point Vector;

struct Point {
    ll x,y;
    Point(){}
    Point(ll _x,ll _y):x(_x),y(_y){}
    ll how_many_points(Point p){
        int g=__gcd(abs(x-p.x),abs(y-p.y));
        return g+1;
    }

    Vector operator-(Vector v){
        return Vector(x-v.x,y-v.y);
    }

    ll cross(Vector p){
        return x*p.y-y*p.x;
    }
};


ll n,m,p;
int main() {
    scanf("%lld%lld%lld",&n,&m,&p);

    Point O(0,0);
    Point A(n,m);
    Point B(p,0);

    Vector _A=(A-O);
    Vector _B=(B-O);

    ll _2S=abs(_A.cross(_B));
    ll b=(O.how_many_points(A)+A.how_many_points(B)+B.how_many_points(O))-3;
    ll _2a=_2S-b+2;

    printf("%lld\n",_2a/2ll);
}