Dreams of Lawa

In the mystical land of Mosuo where legends tell of a lake called Lugu, TeaTea embarks on a surreal quest within Lugu Lake to find her elusive dream. Her n dreams are arranged in a sequence, each representing a Lawa with a non-negative beauty score a_i. To distinguish these Lawa, TeaTea assigns the i-th Lawa from the left a beauty score of a_i (a non-negative integer).

TeaTea will perform m operations. In each operation, she is given two numbers, p and x. She applies a bitwise XOR with x to both a_p and a_p+1 (i.e. she sets a_p = a_p \oplus x and a_p+1 = a_p+1 \oplus x, where \(\oplus\) denotes the bitwise XOR operation, equivalent to C++'s ^ operator).

After each operation, TeaTea wants to determine how many subarrays (contiguous intervals) \([l,r]\) with \(l \le r\) have an XOR sum equal to zero. The XOR sum of a subarray \([l,r]\) is given by

\[a_l \oplus a_{l+1} \oplus \dots \oplus a_r\]

Two subarrays are considered different if their endpoints differ.

To avoid large outputs, instead of printing the answer for each operation, output four integers:

• The bitwise XOR of all the answers.
• The count of answers that are odd.
• The maximum answer among all operations.
• The minimum answer among all operations.

Note: All formulas are represented in LaTeX format.

inputFormat

The first line contains two integers \(n\) and \(m\) \((1 \leq n, m \leq \text{small limits})\), representing the number of dreams and the number of operations respectively.

The second line contains \(n\) non-negative integers \(a_1, a_2, \dots, a_n\) representing the beauty scores of the dreams.

Each of the following \(m\) lines contains two integers \(p\) and \(x\) \((1 \leq p < n,\; 0 \leq x \leq \text{some limit})\), describing an operation where both \(a_p\) and \(a_{p+1}\) are updated as \(a_p = a_p \oplus x\) and \(a_{p+1} = a_{p+1} \oplus x\).

outputFormat

Output four integers separated by spaces:

• The XOR of all the answers obtained after each operation.
• The total number of answers that are odd.
• The maximum answer among all operations.
• The minimum answer among all operations.

sample

3 2
1 2 3
1 1
2 2

0 2 3 3