#include <bits/stdc++.h>
using namespace std;
long long a[1000000][2];
int main() {
  long long X = 0, Y = 0;
  long long n, j;
  cin >> n >> j;
  long long x, y;
  cin >> x >> y;
  long long Xneg = 0, Yneg = 0;
  long long Xpos = 0, Ypos = 0;
  bool pos = 1;
  for (long long i = 0; i < n; i++)
    cin >> a[i][0] >> a[i][1], a[i][0] *= 2, a[i][1] *= 2;
  for (long long i = n - 1; i >= 0; i--) {
    if (pos)
      Xpos += a[i][0], Xneg -= a[i][0], Ypos += a[i][1], Yneg -= a[i][1];
    else
      Xpos -= a[i][0], Xneg += a[i][0], Ypos -= a[i][1], Yneg += a[i][1];
    pos = !pos;
  }
  if (n % 2 == 0) {
    long long k = (j - 1) % n;
    long long h = (j - 1) / n;
    pos = 1;
    for (long long i = k; i >= 0; i--) {
      if (pos)
        X += a[i][0], Y += a[i][1];
      else
        X -= a[i][0], Y -= a[i][1];
      pos = !pos;
    }
    if (pos)
      X += Xpos * h, Y += Ypos * h;
    else
      Y += Xneg * h, Y += Yneg * h;
    if (pos)
      X += x, Y += y;
    else
      X -= x, Y -= y;
  } else {
    long long k = (j - 1) % n;
    long long h = (j - 1) / n;
    pos = 1;
    for (long long i = k; i >= 0; i--) {
      if (pos)
        X += a[i][0], Y += a[i][1];
      else
        X -= a[i][0], Y -= a[i][1];
      pos = !pos;
    }
    h = h % 2;
    if (pos)
      X += Xpos * h, Y += Ypos * h;
    else
      X += Xneg * h, Y += Yneg * h;
    if (h % 2) pos = !pos;
    if (pos)
      X += x, Y += y;
    else
      X -= x, Y -= y;
  }
  cout << X << " " << Y << endl;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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;
long long a[1000000][2];
int main() {
  long long X = 0, Y = 0;
  long long n, j;
  cin >> n >> j;
  long long x, y;
  cin >> x >> y;
  long long Xneg = 0, Yneg = 0;
  long long Xpos = 0, Ypos = 0;
  bool pos = 1;
  for (long long i = 0; i < n; i++)
    cin >> a[i][0] >> a[i][1], a[i][0] *= 2, a[i][1] *= 2;
  for (long long i = n - 1; i >= 0; i--) {
    if (pos)
      Xpos += a[i][0], Xneg -= a[i][0], Ypos += a[i][1], Yneg -= a[i][1];
    else
      Xpos -= a[i][0], Xneg += a[i][0], Ypos -= a[i][1], Yneg += a[i][1];
    pos = !pos;
  }
  if (n % 2 == 0) {
    long long k = (j - 1) % n;
    long long h = (j - 1) / n;
    pos = 1;
    for (long long i = k; i >= 0; i--) {
      if (pos)
        X += a[i][0], Y += a[i][1];
      else
        X -= a[i][0], Y -= a[i][1];
      pos = !pos;
    }
    if (pos)
      X += Xpos * h, Y += Ypos * h;
    else
      Y += Xneg * h, Y += Yneg * h;
    if (pos)
      X += x, Y += y;
    else
      X -= x, Y -= y;
  } else {
    long long k = (j - 1) % n;
    long long h = (j - 1) / n;
    pos = 1;
    for (long long i = k; i >= 0; i--) {
      if (pos)
        X += a[i][0], Y += a[i][1];
      else
        X -= a[i][0], Y -= a[i][1];
      pos = !pos;
    }
    h = h % 2;
    if (pos)
      X += Xpos * h, Y += Ypos * h;
    else
      X += Xneg * h, Y += Yneg * h;
    if (h % 2) pos = !pos;
    if (pos)
      X += x, Y += y;
    else
      X -= x, Y -= y;
  }
  cout << X << " " << Y << endl;
}

```