对合排列 - 問題

#10931. 对合排列

統計

この問題は以下のコンテストで使用されています：

Elegia's Forgotten Hill

This problem is prepared by Elegia .

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：

所有长度为 $n$ 的对合排列中，逆序对个数 $=u$ 的排列个数 mod 2。

输入格式

一行两个整数，$n,k$。

输出格式

一行一个长度为 $n$ 的01串，表示每个 $u\in [0,k]$ 的输出。

样例数据

样例输入

3 9

样例输出

1001000000

子任务

对于 $100\%$ 的数据，$1 \leq k, n \leq 10^6$

测试点	$n \leq$	$k \leq $
$1 \sim 2$	$10$	$50$
$3 \sim 4$	$20$	$200$
$5 \sim 7$	$2\,000$	$2 \times 10^5$
$8$		$5 \times 10^5$
$9\sim 10$		$10^6$
$11 \sim 14$	$10^6$	$5 \times 10^4$
$15 \sim 20$	$10^6$	$10^6$

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