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我们称一个排列 $p$ 为对合排列当且仅当对于每个 $i$ 有 $p(p(i))=i$。
对于一个给定的正整数 $k$，你需要对于每个 $u\in [0,k]$ 求出：
一行两个整数，$n,k$。
一行一个长度为 $n$ 的01串，表示每个 $u\in [0,k]$ 的输出。
3 9
1001000000
对于 $100\%$ 的数据，$1 \leq k, n \leq 10^6$
| 测试点 | $n \leq$ | $k \leq $ |
|---|---|---|
| $1 \sim 2$ | $10$ | $50$ |
| $3 \sim 4$ | $20$ | $200$ |
| $5 \sim 7$ | $2\,000$ | $2 \times 10^5$ |
| $8$ | $5 \times 10^5$ | |
| $9\sim 10$ | $10^6$ | |
| $11 \sim 14$ | $10^6$ | $5 \times 10^4$ |
| $15 \sim 20$ | $10^6$ |
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