#include <bits/stdc++.h>
using namespace std;
using ll = long long;
struct point {
  ll x, y;
  point(ll _x = 0, ll _y = 0) { x = _x, y = _y; }
  point operator+(const point &p) { return {x + p.x, y + p.y}; }
  point operator-(const point &p) { return {x - p.x, y - p.y}; }
  point operator*(long long m) { return {x * m, y * m}; }
  void scan() { scanf("%lld%lld", &x, &y); }
};
int main() {
  ll n, j;
  point m, ans, pt;
  scanf("%lld%lld", &n, &j);
  j--;
  j %= 2 * n;
  m.scan();
  auto coef = [&](ll i) {
    if (j < i || j >= i + n) return 0;
    if (j % 2 == i % 2) return 1;
    return -1;
  };
  for (ll i = 0; i < n; i++) {
    pt.scan();
    ans = ans + (pt - m) * coef(i);
  }
  ans = (ans * 2) + m;
  printf("%lld %lld\n", ans.x, ans.y);
  return 0;
}

### Prompt

Your task is to create a Cpp solution 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;
using ll = long long;
struct point {
  ll x, y;
  point(ll _x = 0, ll _y = 0) { x = _x, y = _y; }
  point operator+(const point &p) { return {x + p.x, y + p.y}; }
  point operator-(const point &p) { return {x - p.x, y - p.y}; }
  point operator*(long long m) { return {x * m, y * m}; }
  void scan() { scanf("%lld%lld", &x, &y); }
};
int main() {
  ll n, j;
  point m, ans, pt;
  scanf("%lld%lld", &n, &j);
  j--;
  j %= 2 * n;
  m.scan();
  auto coef = [&](ll i) {
    if (j < i || j >= i + n) return 0;
    if (j % 2 == i % 2) return 1;
    return -1;
  };
  for (ll i = 0; i < n; i++) {
    pt.scan();
    ans = ans + (pt - m) * coef(i);
  }
  ans = (ans * 2) + m;
  printf("%lld %lld\n", ans.x, ans.y);
  return 0;
}

```