Find Lines

#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<cmath>
#include<algorithm>
#include<map>
#include<set>
#include<vector>
#include<queue>
#include<stack>
//#include<bits/std c++.h>
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
const LL MOD = 1e7 + 7;
const LL maxn = 1e5 + 131;
int gcd(int a,int b) { return b == 0 ? a : gcd(b, a % b); }
unsigned int Rand() { static unsigned seed = 233; return seed = seed * 1000007 + 1;}
struct Line {
    long long a,b,c;
    Line() {}
    Line(int a1,int b1,int a2,int b2) {
        int g = gcd(abs(a1 - a2),abs(b1 - b2));
        if(a1 - a2 < 0) g = -g;
        a = -(b1-b2)/g;
        this->b = (a1-a2) / g;
        this->c = a*a1 + b*b1;
    }
    bool operator < (Line s) const { return (a < s.a || (a == s.a && (b < s.b || (b == s.b && c < s.c))));}
};
map<Line,int> L;
map<Line,int>::iterator it;
int X[100031], Y[100031];
int main() {
    int n,p;
    scanf("%d%d",&n,&p);
    L.clear();
    if(n == 1) {
            printf("possible\n");
            return 0;}
    int limit = n * p;
    for(int i = 0; i < n; ++i) scanf("%d%d",&X[i],&Y[i]);
    for(int t = 0; t < 1000; ++t) { //先随机处理去重 + 统计次数 
        int a = Rand() % n, b = Rand() % n;
        while(a == b) b = Rand() % n;
        L[Line(X[a],Y[a],X[b],Y[b])]++;
    }
    for(it = L.begin(); it != L.end(); ++it)
    {
        if(it->second < 20) continue;//随机1000次，在线上的点应该要出现一定次数 1/25 * 1000， 20保险，然而30 40 WA了... 
        int num = 0;                 //简直拼人品....... 
        long long a = it->first.a, b = it->first.b, c = it->first.c;
        for(int i = 0; i < n; ++i) {
            if(a*X[i] + b*Y[i] == c) {
                num++;
                if(num * 100 >= limit) {
                    printf("possible\n");
                    return 0;
                }
            }
        }
    }
    printf("impossible\n");
    return 0;
}