#include <bits/stdc++.h>
using namespace std;
bool sortbysec(const pair<int, int> &a, const pair<int, int> &b) {
  return (a.second < b.second);
}
long long int containsDigit(long long int number, long long int digit) {
  while (number != 0) {
    int curr_digit = number % 10;
    if (curr_digit == digit) return 1;
    number /= 10;
  }
  return 0;
}
long long int soltn(long long int x, long long int n) {
  if (x >= 0)
    return x % n;
  else
    return n + x % n;
}
long long int bin_srch(long long int L[], long long int N, long long int item) {
  long long int flag = -2;
  int l = 0, u = N - 1, m;
  while (l <= u) {
    m = (l + u) / 2;
    if (item == L[m]) {
      flag = m - 1;
      break;
    } else if (item > L[m])
      l = m - 1;
    else
      u = m + 1;
  }
  return flag;
}
long long int modExp(long long int b, long long int p) {
  long long int res = 1;
  while (p > 0) {
    if (p & 1) {
      res = (res * b) % 1000000007;
    }
    b = (b * b) % 1000000007;
    p >>= 1;
  }
  return res;
}
long long int properdiv(long long int x, long long int y) {
  if (x % y == 0)
    return x / y;
  else
    return x / y + 1;
}
long long int coda(long long int n, long long int d) {
  long long int count = 0;
  while (n != 0) {
    if (n % 10 == d) count++;
    n /= 10;
  }
  return count;
}
long long int minDissame(long long int a[], long long int n) {
  map<long long int, long long int> hmap;
  long long int minDistance = INT_MAX;
  long long int previousIndex = 0, currentIndex = 0;
  for (long long int i = 0; i < n; i++) {
    if (hmap.find(a[i]) != hmap.end()) {
      currentIndex = i;
      previousIndex = hmap[a[i]];
      minDistance = min((currentIndex - previousIndex), minDistance);
    }
    hmap[a[i]] = i;
  }
  return (minDistance == INT_MAX ? -1 : minDistance);
}
long long int minDistanytwo(long long int arr[], long long int n,
                            long long int x, long long int y) {
  long long int p = -1, min_dist = INT_MAX;
  for (long long int i = 0; i < n; i++) {
    if (arr[i] == x || arr[i] == y) {
      if (p != -1 && arr[i] != arr[p]) min_dist = min(min_dist, i - p);
      p = i;
    }
  }
  if (min_dist == INT_MAX) return -1;
  return min_dist;
}
long long int mdls(long long int x) { return max(x, -x); }
long long int pow1(long long int n, long long int p) {
  if (p == 0) return 1;
  long long int x = pow1(n, p / 2);
  x = (x * x) % 1000000007;
  if (p % 2 == 0)
    return x;
  else
    return (x * n) % 1000000007;
}
string fumn(string s) {
  string p;
  for (long long int i = 0; i < s.length(); i++)
    if (isalpha(s[i])) p += toupper(s[i]);
  return p;
}
long long int turns(string S, string SS) {
  long long int i, cc = 0, l = S.length();
  for (long long int i = 0; i < l; i++) {
    if (S[i] != SS[i]) cc++;
  }
  return cc / 2;
}
long double polygonArea(long double X[], long double Y[], long long int n) {
  double area = 0.0;
  long long int j = n - 1;
  for (long long int i = 0; i < n; i++) {
    area += (X[j] + X[i]) * (Y[j] - Y[i]);
    j = i;
  }
  return abs(area / 2.0);
}
long long int isSubstr(string s1, string s2) {
  long long int M = s1.length();
  long long int N = s2.length();
  for (long long int i = 0; i <= N - M; i++) {
    long long int j;
    for (j = 0; j < M; j++)
      if (s2[i + j] != s1[j]) break;
    if (j == M) return i;
  }
  return -1;
}
long long int hhh2(unsigned long long int n) {
  if (n < 1) return 0;
  long long int res = 1;
  long long int u = 0;
  for (long long int i = 0; i < 8 * sizeof(unsigned long long int); i++) {
    long long int curr = 1 << i;
    if (curr > n) break;
    u++;
    res = curr;
  }
  return u;
}
long double ldgcd(long double a, long double b) {
  return a < 0.0001 ? b : ldgcd(fmod(b, a), a);
}
void onesol(long long int a, long long int b, long long int &x,
            long long int &y, long long int &g) {
  if (!b) {
    g = a;
    x = 1;
    y = 0;
  } else {
    onesol(b, a % b, y, x, g);
    y -= a / b * x;
  }
}
long long int gcd(long long int a, long long int b, long long int &x,
                  long long int &y) {
  if (a == 0) {
    x = 0;
    y = 1;
    return b;
  }
  long long int x1, y1;
  long long int d = gcd(b % a, a, x1, y1);
  x = y1 - (b / a) * x1;
  y = x1;
  return d;
}
bool find_any_solution(long long int a, long long int b, long long int c,
                       long long int &x0, long long int &y0, long long int &g) {
  g = gcd(llabs(a), llabs(b), x0, y0);
  if (c % g) {
    return false;
  }
  x0 *= c / g;
  y0 *= c / g;
  if (a < 0) x0 = -x0;
  if (b < 0) y0 = -y0;
  return true;
}
void shift_solution(long long int &x, long long int &y, long long int a,
                    long long int b, long long int cnt) {
  x += cnt * b;
  y -= cnt * a;
}
long long int find_all_solutions(long long int a, long long int b,
                                 long long int c, long long int minx,
                                 long long int maxx, long long int miny,
                                 long long int maxy) {
  long long int x, y, g;
  if (!find_any_solution(a, b, c, x, y, g)) return 0;
  a /= g;
  b /= g;
  long long int sign_a = a > 0 ? +1 : -1;
  long long int sign_b = b > 0 ? +1 : -1;
  shift_solution(x, y, a, b, (minx - x) / b);
  if (x < minx) shift_solution(x, y, a, b, sign_b);
  if (x > maxx) return 0;
  long long int lx1 = x;
  shift_solution(x, y, a, b, (maxx - x) / b);
  if (x > maxx) shift_solution(x, y, a, b, -sign_b);
  long long int rx1 = x;
  shift_solution(x, y, a, b, -(miny - y) / a);
  if (y < miny) shift_solution(x, y, a, b, -sign_a);
  if (y > maxy) return 0;
  long long int lx2 = x;
  shift_solution(x, y, a, b, -(maxy - y) / a);
  if (y > maxy) shift_solution(x, y, a, b, sign_a);
  long long int rx2 = x;
  if (lx2 > rx2) swap(lx2, rx2);
  long long int lx = max(lx1, lx2);
  long long int rx = min(rx1, rx2);
  if (lx > rx) return 0;
  return (rx - lx) / llabs(b) + 1;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  long long int t = 1;
  while (t--) {
    vector<pair<long long int, long long int> > v;
    long long int n, m, i, k, v1, v2, j, l;
    cin >> n >> m;
    long long int a[n], b[n];
    cin >> v1 >> v2;
    v.push_back(make_pair(v1, v2));
    for (long long int i = 0; i < n; i++) cin >> a[i] >> b[i];
    m = m % (2 * n);
    for (long long int i = 0; i < n * 2; i++) {
      v1 = 2 * a[i % n] - v[i].first;
      v2 = 2 * b[i % n] - v[i].second;
      v.push_back(make_pair(v1, v2));
    }
    cout << v[m].first << " " << v[m].second;
    cout << "\n";
  }
  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;
bool sortbysec(const pair<int, int> &a, const pair<int, int> &b) {
  return (a.second < b.second);
}
long long int containsDigit(long long int number, long long int digit) {
  while (number != 0) {
    int curr_digit = number % 10;
    if (curr_digit == digit) return 1;
    number /= 10;
  }
  return 0;
}
long long int soltn(long long int x, long long int n) {
  if (x >= 0)
    return x % n;
  else
    return n + x % n;
}
long long int bin_srch(long long int L[], long long int N, long long int item) {
  long long int flag = -2;
  int l = 0, u = N - 1, m;
  while (l <= u) {
    m = (l + u) / 2;
    if (item == L[m]) {
      flag = m - 1;
      break;
    } else if (item > L[m])
      l = m - 1;
    else
      u = m + 1;
  }
  return flag;
}
long long int modExp(long long int b, long long int p) {
  long long int res = 1;
  while (p > 0) {
    if (p & 1) {
      res = (res * b) % 1000000007;
    }
    b = (b * b) % 1000000007;
    p >>= 1;
  }
  return res;
}
long long int properdiv(long long int x, long long int y) {
  if (x % y == 0)
    return x / y;
  else
    return x / y + 1;
}
long long int coda(long long int n, long long int d) {
  long long int count = 0;
  while (n != 0) {
    if (n % 10 == d) count++;
    n /= 10;
  }
  return count;
}
long long int minDissame(long long int a[], long long int n) {
  map<long long int, long long int> hmap;
  long long int minDistance = INT_MAX;
  long long int previousIndex = 0, currentIndex = 0;
  for (long long int i = 0; i < n; i++) {
    if (hmap.find(a[i]) != hmap.end()) {
      currentIndex = i;
      previousIndex = hmap[a[i]];
      minDistance = min((currentIndex - previousIndex), minDistance);
    }
    hmap[a[i]] = i;
  }
  return (minDistance == INT_MAX ? -1 : minDistance);
}
long long int minDistanytwo(long long int arr[], long long int n,
                            long long int x, long long int y) {
  long long int p = -1, min_dist = INT_MAX;
  for (long long int i = 0; i < n; i++) {
    if (arr[i] == x || arr[i] == y) {
      if (p != -1 && arr[i] != arr[p]) min_dist = min(min_dist, i - p);
      p = i;
    }
  }
  if (min_dist == INT_MAX) return -1;
  return min_dist;
}
long long int mdls(long long int x) { return max(x, -x); }
long long int pow1(long long int n, long long int p) {
  if (p == 0) return 1;
  long long int x = pow1(n, p / 2);
  x = (x * x) % 1000000007;
  if (p % 2 == 0)
    return x;
  else
    return (x * n) % 1000000007;
}
string fumn(string s) {
  string p;
  for (long long int i = 0; i < s.length(); i++)
    if (isalpha(s[i])) p += toupper(s[i]);
  return p;
}
long long int turns(string S, string SS) {
  long long int i, cc = 0, l = S.length();
  for (long long int i = 0; i < l; i++) {
    if (S[i] != SS[i]) cc++;
  }
  return cc / 2;
}
long double polygonArea(long double X[], long double Y[], long long int n) {
  double area = 0.0;
  long long int j = n - 1;
  for (long long int i = 0; i < n; i++) {
    area += (X[j] + X[i]) * (Y[j] - Y[i]);
    j = i;
  }
  return abs(area / 2.0);
}
long long int isSubstr(string s1, string s2) {
  long long int M = s1.length();
  long long int N = s2.length();
  for (long long int i = 0; i <= N - M; i++) {
    long long int j;
    for (j = 0; j < M; j++)
      if (s2[i + j] != s1[j]) break;
    if (j == M) return i;
  }
  return -1;
}
long long int hhh2(unsigned long long int n) {
  if (n < 1) return 0;
  long long int res = 1;
  long long int u = 0;
  for (long long int i = 0; i < 8 * sizeof(unsigned long long int); i++) {
    long long int curr = 1 << i;
    if (curr > n) break;
    u++;
    res = curr;
  }
  return u;
}
long double ldgcd(long double a, long double b) {
  return a < 0.0001 ? b : ldgcd(fmod(b, a), a);
}
void onesol(long long int a, long long int b, long long int &x,
            long long int &y, long long int &g) {
  if (!b) {
    g = a;
    x = 1;
    y = 0;
  } else {
    onesol(b, a % b, y, x, g);
    y -= a / b * x;
  }
}
long long int gcd(long long int a, long long int b, long long int &x,
                  long long int &y) {
  if (a == 0) {
    x = 0;
    y = 1;
    return b;
  }
  long long int x1, y1;
  long long int d = gcd(b % a, a, x1, y1);
  x = y1 - (b / a) * x1;
  y = x1;
  return d;
}
bool find_any_solution(long long int a, long long int b, long long int c,
                       long long int &x0, long long int &y0, long long int &g) {
  g = gcd(llabs(a), llabs(b), x0, y0);
  if (c % g) {
    return false;
  }
  x0 *= c / g;
  y0 *= c / g;
  if (a < 0) x0 = -x0;
  if (b < 0) y0 = -y0;
  return true;
}
void shift_solution(long long int &x, long long int &y, long long int a,
                    long long int b, long long int cnt) {
  x += cnt * b;
  y -= cnt * a;
}
long long int find_all_solutions(long long int a, long long int b,
                                 long long int c, long long int minx,
                                 long long int maxx, long long int miny,
                                 long long int maxy) {
  long long int x, y, g;
  if (!find_any_solution(a, b, c, x, y, g)) return 0;
  a /= g;
  b /= g;
  long long int sign_a = a > 0 ? +1 : -1;
  long long int sign_b = b > 0 ? +1 : -1;
  shift_solution(x, y, a, b, (minx - x) / b);
  if (x < minx) shift_solution(x, y, a, b, sign_b);
  if (x > maxx) return 0;
  long long int lx1 = x;
  shift_solution(x, y, a, b, (maxx - x) / b);
  if (x > maxx) shift_solution(x, y, a, b, -sign_b);
  long long int rx1 = x;
  shift_solution(x, y, a, b, -(miny - y) / a);
  if (y < miny) shift_solution(x, y, a, b, -sign_a);
  if (y > maxy) return 0;
  long long int lx2 = x;
  shift_solution(x, y, a, b, -(maxy - y) / a);
  if (y > maxy) shift_solution(x, y, a, b, sign_a);
  long long int rx2 = x;
  if (lx2 > rx2) swap(lx2, rx2);
  long long int lx = max(lx1, lx2);
  long long int rx = min(rx1, rx2);
  if (lx > rx) return 0;
  return (rx - lx) / llabs(b) + 1;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  long long int t = 1;
  while (t--) {
    vector<pair<long long int, long long int> > v;
    long long int n, m, i, k, v1, v2, j, l;
    cin >> n >> m;
    long long int a[n], b[n];
    cin >> v1 >> v2;
    v.push_back(make_pair(v1, v2));
    for (long long int i = 0; i < n; i++) cin >> a[i] >> b[i];
    m = m % (2 * n);
    for (long long int i = 0; i < n * 2; i++) {
      v1 = 2 * a[i % n] - v[i].first;
      v2 = 2 * b[i % n] - v[i].second;
      v.push_back(make_pair(v1, v2));
    }
    cout << v[m].first << " " << v[m].second;
    cout << "\n";
  }
  return 0;
}

```