Problem:
Score : 700 points

Problem Statement

Snuke is playing a puzzle game.
In this game, you are given a rectangular board of dimensions R × C, filled with numbers. Each integer i from 1 through N is written twice, at the coordinates (x_{i,1},y_{i,1}) and (x_{i,2},y_{i,2}).

The objective is to draw a curve connecting the pair of points where the same integer is written, for every integer from 1 through N.
Here, the curves may not go outside the board or cross each other.

Determine whether this is possible.

Constraints

1 ≤ R,C ≤ 10^8

1 ≤ N ≤ 10^5

0 ≤ x_{i,1},x_{i,2} ≤ R(1 ≤ i ≤ N)

0 ≤ y_{i,1},y_{i,2} ≤ C(1 ≤ i ≤ N)

All given points are distinct.

All input values are integers.

Input

Input is given from Standard Input in the following format:

R C N
x_{1,1} y_{1,1} x_{1,2} y_{1,2}
:
x_{N,1} y_{N,1} x_{N,2} y_{N,2}

Output

Print YES if the objective is achievable; print NO otherwise.

Sample Input 1

4 2 3
0 1 3 1
1 1 4 1
2 0 2 2

Sample Output 1

YES

The above figure shows a possible solution.

Sample Input 2

2 2 4
0 0 2 2
2 0 0 1
0 2 1 2
1 1 2 1

Sample Output 2

NO

Sample Input 3

5 5 7
0 0 2 4
2 3 4 5
3 5 5 2
5 5 5 4
0 3 5 1
2 2 4 4
0 5 4 1

Sample Output 3

YES

Sample Input 4

1 1 2
0 0 1 1
1 0 0 1

Sample Output 4

NO

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <iostream>
#include <string>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <algorithm>
#include <set>
#include <sstream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <cctype>
#include <climits>
#include <list>
#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define ALL(x) (x).begin(),(x).end()

using namespace std;
int R,C,N;

int length(int x,int y){
    if(y==0){
        return x;
    }
    if(x==0){
        return 2*(R+C)-y;
    }
    if(x==R){
        return R+y;
    }
    return 2*R+C-x;
}

int main() {
    cin>>R>>C>>N;

    int passed[2*(R+C)+1];
 //   fill(passed,passed+2*(R+C),-1);

    REP(i,N){
        int x1,y1,x2,y2;
        cin>>x1>>y1>>x2>>y2;
        if ((x1%R==0||y1%C==0)&&(x2%R==0||y2%C==0)){
            passed[length(x1,y1)]=i+1;
            passed[length(x2,y2)]=i+1;
        }
    }



    stack<int> pos;
    pos.push(-1);

    REP(i,2*(R+C)) {
        if (passed[i] >= 0) {
            if(pos.top()!=passed[i]){
                pos.push(passed[i]);
            }else{
                pos.pop();
                }
            }
    }

    if(pos.size()==1){
        cout<<"YES"<<endl;
    }else{
        cout<<"NO"<<endl;
    }
    return 0;
}