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C. Sequence of points

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given the following points with integer coordinates on the plane: *M*_{0}, *A*_{0}, *A*_{1}, ..., *A*_{n - 1}, where *n* is odd number. Now we define the following infinite sequence of points *M*_{i}: *M*_{i} is symmetric to *M*_{i - 1} according (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 *M*_{j}.

Input

On the first line you will be given an integer *n* (1 ≤ *n* ≤ 10^{5}), which will be odd, and *j* (1 ≤ *j* ≤ 10^{18}), where *j* is the index of the desired point. The next line contains two space separated integers, the coordinates of *M*_{0}. After that *n* lines follow, where the *i*-th line contain the space separated integer coordinates of the point *A*_{i - 1}. The absolute values of all input coordinates will not be greater then 1000.

Output

On a single line output the coordinates of *M*_{j}, 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

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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