As much as ButaneBot's newly recoded OR function is cool, he is still getting bored of storing only numbers in the form ~2^x-1~ inside of him. Instead, he has been asked to code a much more interesting problem. There are initially ~N~ numbers in an array, and ~Q~ queries of the form ~i~ ~X~. After each query, the ~i~-th number in the array becomes ~X~. Your job is to find the maximum bitwise OR of ANY consecutive subarray, after every single query. Note that ButaneBot is assuming all numbers are represented as a 32-bit signed two's complement number, and that updates are cumulative. He also assumes that your subarray will be of length at least ~1~.

Input Specification

The first line of input will contain the integers ~N~ and ~Q~.

The next line will contain ~N~ integers, the initial array.

The next ~Q~ lines will each have two numbers ~i~ and ~X~ which represent the index to be changed and the value of the new number, respectively.

Constraints

~N \le 10^5~

~Q \le 4 \cdot 10^5~

~1 \le i \le N~

At any time, all values in the array will fall in the range ~[-10^9,10^9]~.

Subtask 1 [30%]

All integers in the input will be either strictly non negative, or strictly non positive.

Subtask 2 [70%]

No additional constraints.

Output Specification

Output one integer for each query, the maximum bitwise OR of any consecutive subarray given the current state of the array.

Sample Input

3 2
2 3 -1
3 -2
1 -4

Sample Output

3
3

Explanation for Sample Output

The initial array is ~[2,3,-1]~. After the first update, the array becomes ~[2,3,-2]~. The maximum bitwise OR of a subarray is ~2 \mathbin{|} 3=3~. After the second update, our array becomes ~[-4,3,-2]~. In this case, the best bitwise OR we can get is choosing just the number ~3~.