#include <bits/stdc++.h>
using namespace std;
template <class T>
inline int countbit(T n) {
  return (n == 0) ? 0 : (1 + countbit(n & (n - 1)));
}
template <class T>
inline T gcd(T a, T b) {
  return b ? gcd(b, a % b) : a;
}
const double EPS = 1e-9;
const double PI = acos(-1.0);
pair<int, int> next(pair<int, int> m, pair<int, int> a) {
  pair<int, int> n;
  n.first = 2 * a.first - m.first;
  n.second = 2 * a.second - m.second;
  return n;
}
int main(void) {
  int n;
  long long j;
  cin >> n >> j;
  vector<pair<int, int> > as(n, pair<int, int>(0, 0));
  vector<pair<int, int> > ms(n * 2, pair<int, int>(0, 0));
  cin >> ms[0].first >> ms[0].second;
  for (int i = 0; i < int(n); i++) {
    cin >> as[i].first >> as[i].second;
  }
  int i = 1;
  while (i < n * 2) {
    ms[i] = next(ms[i - 1], as[(i - 1) % n]);
    i++;
  }
  cout << ms[j % (n * 2)].first << " " << ms[j % (n * 2)].second << endl;
  return 0;
}

### Prompt

Create a solution in cpp for the following problem:

You are given the following points with integer coordinates on the plane: M0, A0, A1, ..., An - 1, where n is odd number. Now we define the following infinite sequence of points Mi: Mi is symmetric to Mi - 1 according <image> (for every natural number i). Here point B is symmetric to A according M, if M is the center of the line segment AB. Given index j find the point Mj.

Input

On the first line you will be given an integer n (1 ≤ n ≤ 105), which will be odd, and j (1 ≤ j ≤ 1018), where j is the index of the desired point. The next line contains two space separated integers, the coordinates of M0. After that n lines follow, where the i-th line contain the space separated integer coordinates of the point Ai - 1. The absolute values of all input coordinates will not be greater then 1000.

Output

On a single line output the coordinates of Mj, space separated.

Examples

Input

3 4
0 0
1 1
2 3
-5 3


Output

14 0


Input

3 1
5 5
1000 1000
-1000 1000
3 100


Output

1995 1995

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <class T>
inline int countbit(T n) {
  return (n == 0) ? 0 : (1 + countbit(n & (n - 1)));
}
template <class T>
inline T gcd(T a, T b) {
  return b ? gcd(b, a % b) : a;
}
const double EPS = 1e-9;
const double PI = acos(-1.0);
pair<int, int> next(pair<int, int> m, pair<int, int> a) {
  pair<int, int> n;
  n.first = 2 * a.first - m.first;
  n.second = 2 * a.second - m.second;
  return n;
}
int main(void) {
  int n;
  long long j;
  cin >> n >> j;
  vector<pair<int, int> > as(n, pair<int, int>(0, 0));
  vector<pair<int, int> > ms(n * 2, pair<int, int>(0, 0));
  cin >> ms[0].first >> ms[0].second;
  for (int i = 0; i < int(n); i++) {
    cin >> as[i].first >> as[i].second;
  }
  int i = 1;
  while (i < n * 2) {
    ms[i] = next(ms[i - 1], as[(i - 1) % n]);
    i++;
  }
  cout << ms[j % (n * 2)].first << " " << ms[j % (n * 2)].second << endl;
  return 0;
}

```