#include <bits/stdc++.h>
using namespace std;
struct Point {
  int x, y;
};
int main() {
  int n;
  long long k;
  cin >> n >> k;
  vector<Point> a(n);
  vector<Point> m(1);
  map<pair<int, pair<int, int> >, int> cache;
  cin >> m[0].x >> m[0].y;
  cache[make_pair(0, make_pair(m[0].x, m[0].y))] = 0;
  for (int i = (0); i < ((n)); ++i) cin >> a[i].x >> a[i].y;
  long long cycleLength = 0;
  for (int i = 1; i <= k + 1; ++i) {
    Point const& last = m[i - 1];
    Point const& p = a[(i - 1) % n];
    Point next = {p.x + (p.x - last.x), p.y + (p.y - last.y)};
    m.push_back(next);
    if (cache.count(make_pair(i % n, make_pair(next.x, next.y)))) {
      if (!(next.x == m[0].x && next.y == m[0].y)) throw 10;
      k -= cache[make_pair(i % n, make_pair(next.x, next.y))];
      cycleLength = i - cache[make_pair(i % n, make_pair(next.x, next.y))];
      break;
    }
    cache[make_pair(i % n, make_pair(next.x, next.y))] = i;
  }
  if (cycleLength) k %= cycleLength;
  cout << m[k].x << " " << m[k].y << "\n";
  return 0;
}

### Prompt

In cpp, your task is to solve 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;
struct Point {
  int x, y;
};
int main() {
  int n;
  long long k;
  cin >> n >> k;
  vector<Point> a(n);
  vector<Point> m(1);
  map<pair<int, pair<int, int> >, int> cache;
  cin >> m[0].x >> m[0].y;
  cache[make_pair(0, make_pair(m[0].x, m[0].y))] = 0;
  for (int i = (0); i < ((n)); ++i) cin >> a[i].x >> a[i].y;
  long long cycleLength = 0;
  for (int i = 1; i <= k + 1; ++i) {
    Point const& last = m[i - 1];
    Point const& p = a[(i - 1) % n];
    Point next = {p.x + (p.x - last.x), p.y + (p.y - last.y)};
    m.push_back(next);
    if (cache.count(make_pair(i % n, make_pair(next.x, next.y)))) {
      if (!(next.x == m[0].x && next.y == m[0].y)) throw 10;
      k -= cache[make_pair(i % n, make_pair(next.x, next.y))];
      cycleLength = i - cache[make_pair(i % n, make_pair(next.x, next.y))];
      break;
    }
    cache[make_pair(i % n, make_pair(next.x, next.y))] = i;
  }
  if (cycleLength) k %= cycleLength;
  cout << m[k].x << " " << m[k].y << "\n";
  return 0;
}

```