#include <bits/stdc++.h>
using namespace std;
const long long mod7 = 1000000007;
const long long mod9 = 1000000009;
const int linf = 2000000000;
const long long llinf = 1000000000000000000ll;
ifstream in("series.in");
ofstream out("series.out");
pair<int, int> arr[1000001];
pair<int, int> data[1000001];
pair<int, int> next(pair<int, int> a, pair<int, int> b) {
  pair<int, int> c = make_pair(b.first - a.first, b.second - a.second);
  b.first += c.first;
  b.second += c.second;
  return b;
}
int main() {
  long long n, m;
  cin >> n >> m;
  m %= 2 * n;
  cin >> arr[0].first >> arr[0].second;
  for (int i = 0; i < n; ++i) cin >> data[i].first >> data[i].second;
  for (int i = 0; i <= m; ++i) {
    arr[i + 1] = next(arr[i], data[i % n]);
  }
  cout << arr[m].first << ' ' << arr[m].second;
  return 0;
}

### Prompt

Please create a solution in cpp to 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;
const long long mod7 = 1000000007;
const long long mod9 = 1000000009;
const int linf = 2000000000;
const long long llinf = 1000000000000000000ll;
ifstream in("series.in");
ofstream out("series.out");
pair<int, int> arr[1000001];
pair<int, int> data[1000001];
pair<int, int> next(pair<int, int> a, pair<int, int> b) {
  pair<int, int> c = make_pair(b.first - a.first, b.second - a.second);
  b.first += c.first;
  b.second += c.second;
  return b;
}
int main() {
  long long n, m;
  cin >> n >> m;
  m %= 2 * n;
  cin >> arr[0].first >> arr[0].second;
  for (int i = 0; i < n; ++i) cin >> data[i].first >> data[i].second;
  for (int i = 0; i <= m; ++i) {
    arr[i + 1] = next(arr[i], data[i % n]);
  }
  cout << arr[m].first << ' ' << arr[m].second;
  return 0;
}

```