Migrated from Lutece 332 Sequence of points

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Description

You are given the following points with integer coordinates on the plane: $M_0, A_0, A_1, \cdots , A_{n - 1}$, 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 $A_{(i-1)\rm\ mod\ n}$(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

There are multi-cases. On the first line of each case, you will be given an integer $n$ ($1\leq  n\leq  10^5$), which will be odd, and $j$ ($1\leq  j \leq  10^{18}$), 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

For each case output the coordinates of $M_j$, space separated.

Samples

3 4
0 0
1 1
2 3
-5 3
3 1
5 5
1000 1000
-1000 1000
3 100

14 0
1995 1995

Resources

2011寒假训练（一）(Not Original)