Xenia and Bit Operations

题意翻译

有$2^n$个数，有$m$个操作，每次修改一个数，然后你要输出$\ \ \ \ \ $( (a1|a2)xor(a3|a4) )|( (a5|a6)xor(a7|a8) ).... 即$\ or\ \ \ xor\ $交替计算。 第一行两个数字$n,m$。 第二行$2^n$个数字。 下面$m$行，每行两个数字$x,y$，将第$x$个数字改为$y$。 保证$1\le n \le 17\ , \ 1\le m \le 10^5$，数字任意时刻满足$0\le y \le 2^{30}$ 共$m$行，输出每次改完数字后上述表达式的值。

题目描述

Xenia the beginner programmer has a sequence $ a $ , consisting of $ 2^{n} $ non-negative integers: $ a_{1},a_{2},...,a_{2^{n}} $ . Xenia is currently studying bit operations. To better understand how they work, Xenia decided to calculate some value $ v $ for $ a $ . Namely, it takes several iterations to calculate value $ v $ . At the first iteration, Xenia writes a new sequence $ a_{1} or a_{2},a_{3} or a_{4},...,a_{2^{n}-1} or a_{2^{n}} $ , consisting of $ 2^{n-1} $ elements. In other words, she writes down the bit-wise OR of adjacent elements of sequence $ a $ . At the second iteration, Xenia writes the bitwise exclusive OR of adjacent elements of the sequence obtained after the first iteration. At the third iteration Xenia writes the bitwise OR of the adjacent elements of the sequence obtained after the second iteration. And so on; the operations of bitwise exclusive OR and bitwise OR alternate. In the end, she obtains a sequence consisting of one element, and that element is $ v $ . Let's consider an example. Suppose that sequence $ a=(1,2,3,4) $ . Then let's write down all the transformations $ (1,2,3,4) $ $ → $ $ (1 or 2=3,3 or 4=7) $ $ → $ $ (3 xor 7=4) $ . The result is $ v=4 $ . You are given Xenia's initial sequence. But to calculate value $ v $ for a given sequence would be too easy, so you are given additional $ m $ queries. Each query is a pair of integers $ p,b $ . Query $ p,b $ means that you need to perform the assignment $ a_{p}=b $ . After each query, you need to print the new value $ v $ for the new sequence $ a $ .

输入输出格式

输入格式

The first line contains two integers $ n $ and $ m $ $ (1<=n<=17,1<=m<=10^{5}) $ . The next line contains $ 2^{n} $ integers $ a_{1},a_{2},...,a_{2^{n}} $ $ (0<=a_{i}&lt;2^{30}) $ . Each of the next $ m $ lines contains queries. The $ i $ -th line contains integers $ p_{i},b_{i} $ $ (1<=p_{i}<=2^{n},0<=b_{i}&lt;2^{30}) $ — the $ i $ -th query.

输出格式

Print $ m $ integers — the $ i $ -th integer denotes value $ v $ for sequence $ a $ after the $ i $ -th query.

输入输出样例

输入样例 #1

2 4
1 6 3 5
1 4
3 4
1 2
1 2

输出样例 #1

1
3
3
3

说明

For more information on the bit operations, you can follow this link: http://en.wikipedia.org/wiki/Bitwise\_operation