You are given an array of $n$ integers. Your task is to calculate the bitwise or of each window of $k$ elements, from left to right.

In this problem the input data is large and it is created using a generator.

Input

The first line contains two integers $n$ and $k$: the number of elements and the size of the window.

The next line contains four integers $x$, $a$, $b$ and $c$: the input generator parameters. The input is generated as follows:

• $x_1=x$
• $x_i=(ax_{i-1}+b) \bmod c$ for $i=2,3,\dots,n$

Output

Print the xor of all window ors.

Constraints

• $1 \le k \le n \le 10^7$
• $0 \le x, a, b \le 10^9$
• $1 \le c \le 10^9$

Example

Input:

8 5
3 7 1 11

Output:

4

Explanation: The input array is $[3,0,1,8,2,4,7,6]$. The windows are $[3,0,1,8,2]$, $[0,1,8,2,4]$, $[1,8,2,4,7]$ and $[8,2,4,7,6]$, and their ors are $11$, $15$, $15$ and $15$. Thus, the answer is $11 \oplus 15 \oplus 15 \oplus 15 = 4$.