# [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`