#include <bits/stdc++.h>
using namespace std;
struct Point {
  long long x, y;
  Point operator*(int c) {
    Point ret;
    ret.x = x * c;
    ret.y = y * c;
    return ret;
  }
  void operator+=(Point other) {
    x += other.x;
    y += other.y;
    return;
  }
};
const int MAXN = 100000;
Point M;
Point A[MAXN];
int main() {
  int n;
  long long target;
  Point ans;
  int minus;
  scanf("%d%I64d", &n, &target);
  scanf("%I64d%I64d", &(M.x), &(M.y));
  for (int i = 0; i < n; i++) scanf("%I64d%I64d", &(A[i].x), &(A[i].y));
  target = target % (2 * n);
  ans.x = 0;
  ans.y = 0;
  minus = 1;
  for (int i = (int)target - 1; i >= 0; i--) {
    ans += A[i % n] * minus * 2;
    minus = -minus;
  }
  ans += M * minus;
  printf("%I64d %I64d\n", ans.x, ans.y);
  return 0;
}

### Prompt

Generate 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;
struct Point {
  long long x, y;
  Point operator*(int c) {
    Point ret;
    ret.x = x * c;
    ret.y = y * c;
    return ret;
  }
  void operator+=(Point other) {
    x += other.x;
    y += other.y;
    return;
  }
};
const int MAXN = 100000;
Point M;
Point A[MAXN];
int main() {
  int n;
  long long target;
  Point ans;
  int minus;
  scanf("%d%I64d", &n, &target);
  scanf("%I64d%I64d", &(M.x), &(M.y));
  for (int i = 0; i < n; i++) scanf("%I64d%I64d", &(A[i].x), &(A[i].y));
  target = target % (2 * n);
  ans.x = 0;
  ans.y = 0;
  minus = 1;
  for (int i = (int)target - 1; i >= 0; i--) {
    ans += A[i % n] * minus * 2;
    minus = -minus;
  }
  ans += M * minus;
  printf("%I64d %I64d\n", ans.x, ans.y);
  return 0;
}

```