#include <bits/stdc++.h>
long long solve(long long st, long long x[], long long n, long long step) {
  long long i;
  long long now = st;
  now = st;
  for (i = 0; i < step; i++) {
    if (i && i % n == 0 && now == st) {
      step %= i;
      i = 0;
      if (step == 0) break;
    }
    now += 2 * (x[i % n] - now);
  }
  return now;
}
long long x[100001], y[100001];
int main() {
  long long i, j, k, l, m, n;
  long long sx, sy, ex, ey;
  long long step;
  scanf("%I64lld%I64lld", &n, &step);
  scanf("%I64lld%I64lld", &sx, &sy);
  for (i = 0; i < n; i++) scanf("%I64lld%I64lld", x + i, y + i);
  ex = solve(sx, x, n, step);
  ey = solve(sy, y, n, step);
  printf("%I64lld %I64lld\n", ex, ey);
  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>
long long solve(long long st, long long x[], long long n, long long step) {
  long long i;
  long long now = st;
  now = st;
  for (i = 0; i < step; i++) {
    if (i && i % n == 0 && now == st) {
      step %= i;
      i = 0;
      if (step == 0) break;
    }
    now += 2 * (x[i % n] - now);
  }
  return now;
}
long long x[100001], y[100001];
int main() {
  long long i, j, k, l, m, n;
  long long sx, sy, ex, ey;
  long long step;
  scanf("%I64lld%I64lld", &n, &step);
  scanf("%I64lld%I64lld", &sx, &sy);
  for (i = 0; i < n; i++) scanf("%I64lld%I64lld", x + i, y + i);
  ex = solve(sx, x, n, step);
  ey = solve(sy, y, n, step);
  printf("%I64lld %I64lld\n", ex, ey);
  return 0;
}

```