#include <bits/stdc++.h>
using namespace std;
struct Matrix {
  int m[2][2];
  Matrix operator*(const Matrix &mm) {
    Matrix res;
    res.m[0][0] = m[0][0] * mm.m[0][0] + m[0][1] * mm.m[1][0];
    res.m[0][1] = m[0][0] * mm.m[0][1] + m[0][1] * mm.m[1][1];
    res.m[1][0] = m[1][0] * mm.m[0][0] + m[1][1] * mm.m[1][0];
    res.m[1][1] = m[1][0] * mm.m[0][1] + m[1][1] * mm.m[1][1];
    return res;
  }
};
int main() {
  long long n, j;
  cin >> n >> j;
  pair<int, int> init;
  vector<pair<int, int> > as;
  cin >> init.first >> init.second;
  long long sum_x = 0, sum_y = 0;
  for (int i = 0; i < n; ++i) {
    sum_x *= -1;
    sum_y *= -1;
    int x, y;
    cin >> x >> y;
    sum_x += 2 * x;
    sum_y += 2 * y;
    as.push_back(make_pair(x, y));
  }
  long long loopcnt = j / n;
  long long mod = j % n;
  long long coef_x = sum_x * (loopcnt & 1), coef_y = sum_y * (loopcnt & 1);
  for (int i = 0; i < mod; ++i) {
    coef_x *= -1;
    coef_y *= -1;
    coef_x += 2 * as[i].first;
    coef_y += 2 * as[i].second;
  }
  long long flg = (j & 1) ? -1 : 1;
  cout << init.first * flg + coef_x << ' ' << init.second * flg + coef_y
       << 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;
struct Matrix {
  int m[2][2];
  Matrix operator*(const Matrix &mm) {
    Matrix res;
    res.m[0][0] = m[0][0] * mm.m[0][0] + m[0][1] * mm.m[1][0];
    res.m[0][1] = m[0][0] * mm.m[0][1] + m[0][1] * mm.m[1][1];
    res.m[1][0] = m[1][0] * mm.m[0][0] + m[1][1] * mm.m[1][0];
    res.m[1][1] = m[1][0] * mm.m[0][1] + m[1][1] * mm.m[1][1];
    return res;
  }
};
int main() {
  long long n, j;
  cin >> n >> j;
  pair<int, int> init;
  vector<pair<int, int> > as;
  cin >> init.first >> init.second;
  long long sum_x = 0, sum_y = 0;
  for (int i = 0; i < n; ++i) {
    sum_x *= -1;
    sum_y *= -1;
    int x, y;
    cin >> x >> y;
    sum_x += 2 * x;
    sum_y += 2 * y;
    as.push_back(make_pair(x, y));
  }
  long long loopcnt = j / n;
  long long mod = j % n;
  long long coef_x = sum_x * (loopcnt & 1), coef_y = sum_y * (loopcnt & 1);
  for (int i = 0; i < mod; ++i) {
    coef_x *= -1;
    coef_y *= -1;
    coef_x += 2 * as[i].first;
    coef_y += 2 * as[i].second;
  }
  long long flg = (j & 1) ? -1 : 1;
  cout << init.first * flg + coef_x << ' ' << init.second * flg + coef_y
       << endl;
  return 0;
}

```