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Time Limit: 2 s Memory Limit: 512 MB Total points: 100

#21403. 文艺平衡树

统计

这是一道模板题。

您需要写一种数据结构(可参考题目标题),来维护一个序列,其中需要提供以下操作:

翻转一个区间,例如原有序序列是 5 4 3 2 1,翻转区间是 $ [2, 4] $ 的话,结果是 5 2 3 4 1

Input

第一行为 $ n, m $,$ n $ 表示初始序列有 $ n $ 个数,这个序列依次是 $ \{ 1, 2, \ldots n - 1, n \} $,$ m $ 表示翻转操作次数。

接下来 $ m $ 行每行两个数 $ [l, r] $,数据保证 $ 1 \leq l \leq r \leq n $。

Output

输出一行 $ n $ 个数字,表示原始序列经过 $ m $ 次变换后的结果。

Example

Input

5 3
1 3
1 3
1 4

Output

4 3 2 1 5

Notes

$ 1 \leq n, m \leq 10 ^ 5 $

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