# [ICPC2024 Xi'an I] XOR Game

## 题目背景

# statement updated: \$z\$ is the number of numbers whose values are \$0\$.

## 题目描述

Alice and Bob are playing a game against each other. In front of them are a multiset \$\{a_i\}\$ of non-negative integers and a single integer \$x\$. Each number in \$a\$ is \$0\$ or \$2^i(0\le i<k)\$ before the game. This game will be a turn-based game, and Alice will go first. In one person's turn, he or she will choose an integer from \$a\$. Let this number be \$p\$. Then this person will choose whether or not to make \$x\gets x\oplus p\$, then remove \$p\$ from \$a\$. Here, operation \$\oplus\$ means bitwise xor. Alice wants to make \$x\$ as big as possible, and Bob wants to make \$x\$ as small as possible. You are a bystander who wants to know the final value of \$x\$. However, the size of \$a\$ is a huge number. Formally, there are \$b_i\$ numbers whose values are \$2^i\$ in \$a\$ for all \$0\le i<k\$, and \$z\$ numbers whose values are \$0\$. But you still want to challenge this impossible problem. If Alice and Bob are smart enough, please output the final value of \$x\$.

## 输入输出格式

### 输入格式

The first line contains two integers \$k,z(1\le k\le10^5,0\le z\le 10^9)\$. The next line contains \$k\$ integers, the \$i\$ -th integer is \$b_{i-1}(0\le b_{i-1}\le10^9)\$.

### 输出格式

Output the answer in binary format. Note that you should output exactly \$k\$ digit from high to low even though this number has leading \$0\$s.

## 输入输出样例

### 输入样例 #1

``````1 0
3``````

### 输出样例 #1

``1``

### 输入样例 #2

``````2 0
2 1``````

### 输出样例 #2

``11``

### 输入样例 #3

``````2 0
2 2``````

### 输出样例 #3

``00``