#include <bits/stdc++.h>
using namespace std;
string filename = "test";
vector<pair<int, int> > va;
struct M {
  vector<int> m;
  M() { m = vector<int>(9, 0); }
};
M mult(const M& a, const M& b) {
  M ret;
  for (int _n(3), i(0); i < _n; i++)
    for (int _n(3), j(0); j < _n; j++)
      for (int _n(3), l(0); l < _n; l++) {
        ret.m[i * 3 + j] += (a.m[i * 3 + l] * b.m[l * 3 + j]);
      }
  return ret;
}
M pow(const M& a, unsigned long long p) {
  if (p == 0) {
    M ret;
    ret.m[0] = ret.m[4] = ret.m[8] = 1;
    return ret;
  }
  M m1 = pow(a, p >> 1);
  m1 = mult(m1, m1);
  if (p & 1) m1 = mult(m1, a);
  return m1;
}
int main() {
  int n;
  cin >> n;
  unsigned long long target;
  cin >> target;
  int x, y;
  scanf("%d %d", &x, &y);
  pair<int, int> m0(x, y);
  for (int _n(n), i(0); i < _n; i++) {
    scanf("%d %d", &x, &y);
    va.push_back(pair<int, int>(x, y));
  }
  unsigned long long mod = target % n;
  unsigned long long div = target / n;
  M ret;
  ret.m[0] = ret.m[4] = ret.m[8] = 1;
  for (int _n(n), i(0); i < _n; i++) {
    M mn;
    mn.m[0] = -1;
    mn.m[2] = 2 * va[i].first;
    mn.m[4] = -1;
    mn.m[5] = 2 * va[i].second;
    mn.m[8] = 1;
    ret = mult(mn, ret);
  }
  ret = pow(ret, div);
  for (int _n(mod), i(0); i < _n; i++) {
    M mn;
    mn.m[0] = -1;
    mn.m[2] = 2 * va[i].first;
    mn.m[4] = -1;
    mn.m[5] = 2 * va[i].second;
    mn.m[8] = 1;
    ret = mult(mn, ret);
  }
  long long xx = ret.m[0] * (long long)(m0.first) +
                 ret.m[1] * (long long)(m0.second) + ret.m[2] * (long long)(1);
  long long yy = ret.m[3] * (long long)(m0.first) +
                 ret.m[4] * (long long)(m0.second) + ret.m[5] * (long long)(1);
  cout << xx << " " << yy << endl;
  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;
string filename = "test";
vector<pair<int, int> > va;
struct M {
  vector<int> m;
  M() { m = vector<int>(9, 0); }
};
M mult(const M& a, const M& b) {
  M ret;
  for (int _n(3), i(0); i < _n; i++)
    for (int _n(3), j(0); j < _n; j++)
      for (int _n(3), l(0); l < _n; l++) {
        ret.m[i * 3 + j] += (a.m[i * 3 + l] * b.m[l * 3 + j]);
      }
  return ret;
}
M pow(const M& a, unsigned long long p) {
  if (p == 0) {
    M ret;
    ret.m[0] = ret.m[4] = ret.m[8] = 1;
    return ret;
  }
  M m1 = pow(a, p >> 1);
  m1 = mult(m1, m1);
  if (p & 1) m1 = mult(m1, a);
  return m1;
}
int main() {
  int n;
  cin >> n;
  unsigned long long target;
  cin >> target;
  int x, y;
  scanf("%d %d", &x, &y);
  pair<int, int> m0(x, y);
  for (int _n(n), i(0); i < _n; i++) {
    scanf("%d %d", &x, &y);
    va.push_back(pair<int, int>(x, y));
  }
  unsigned long long mod = target % n;
  unsigned long long div = target / n;
  M ret;
  ret.m[0] = ret.m[4] = ret.m[8] = 1;
  for (int _n(n), i(0); i < _n; i++) {
    M mn;
    mn.m[0] = -1;
    mn.m[2] = 2 * va[i].first;
    mn.m[4] = -1;
    mn.m[5] = 2 * va[i].second;
    mn.m[8] = 1;
    ret = mult(mn, ret);
  }
  ret = pow(ret, div);
  for (int _n(mod), i(0); i < _n; i++) {
    M mn;
    mn.m[0] = -1;
    mn.m[2] = 2 * va[i].first;
    mn.m[4] = -1;
    mn.m[5] = 2 * va[i].second;
    mn.m[8] = 1;
    ret = mult(mn, ret);
  }
  long long xx = ret.m[0] * (long long)(m0.first) +
                 ret.m[1] * (long long)(m0.second) + ret.m[2] * (long long)(1);
  long long yy = ret.m[3] * (long long)(m0.first) +
                 ret.m[4] * (long long)(m0.second) + ret.m[5] * (long long)(1);
  cout << xx << " " << yy << endl;
  return 0;
}

```