십수번의 시도 끝에
평범한 nCr문제가 맞는 거 아닌가
도대체 무엇이 문제란 말인가 하며
좌절하기에 이르렀습니다

아래는 코드입니다.
orz

~~~ c++
#include
#include
#include
#include
using namespace std;

typedef unsigned int uint;
vector< pair, int> > Data;
vector< pair > ans;

inline int min(int a,int b){return a>b?b:a;}
inline int sgn(int a){return a<0?-1:a==0?0:1;}

int main(){
vector bino;
int T;
cin >> T;

int num=0;    
int max_x=0;
while(T--){
    int x1, y1, x2, y2;        
    cin >> x1 >> y1 >> x2 >> y2;
    const int a=x1 - x2;
    const int b=y1 - y2;

    int y, x;        
    if(sgn(a) * sgn(b) >= 0){
        y = abs(a) + abs(b);
        x = abs(b);
    }
    else{            
        if(abs(a) >= abs(b)){
            y = abs(a);
            x = abs(b);
        }
        else{
            y = abs(b);
            x = abs(a+b);
        }
    }

// cout << y << " " << x << endl;
Data.push_back(make_pair(make_pair(y,x), num++));
}
sort(Data.begin(), Data.end());

int i, j, di, last = 0x7fffffff;
bino.push_back(1u);
for(i=di=0; di < Data.size() ;++i){        
    j=bino.size()-2;
    j=min(j, last);

    //cout << j << "\n";
    for(;j>=1;--j){
        bino[j] += bino[j-1];
        if(bino[j] > 0x7fffffffu)
            last = j-1;
    }    
    while(di < Data.size() && Data[di].first.first == i){
        ans.push_back(make_pair(Data[di].second, bino[ Data[di].first.second ]));
        ++di;
    }        
    bino.push_back(1u);
}
sort(ans.begin(), ans.end());
for(i=0;i<ans.size();++i){
    cout << ans[i].second << endl;
}
return 0;

}
~~~