2293: Distribution Center 中南多校

Description

The factory of the Impractically Complicated Products Corporation has many manufacturing lines and the same number of corresponding storage rooms. The same number of conveyor lanes are laid out in parallel to transfer goods from manufacturing lines directly to the corresponding storage rooms. Now, they plan to install a number of robot arms here and there between pairs of adjacent conveyor lanes so that goods in one of the lanes can be picked up and released down on the other, and also in the opposite way. This should allow mixing up goods from different manufacturing lines to the storage rooms. Depending on the positions of robot arms, the goods from each of the manufacturing lines can only be delivered to some of the storage rooms. Your task is to find the number of manufacturing lines from which goods can be transferred to each of the storage rooms, given the number of conveyor lanes and positions of robot arms

Input

The input consists of a single test case, formatted as follows.
n m
x1 y1
.
.
.
xm ym
An integer n (2 ≤ n ≤ 200000) in the first line is the number of conveyor lanes. The lanes are numbered from 1 to n, and two lanes with their numbers differing with 1 are adjacent. All of them start from the position x = 0 and end at x = 100000. The other integer m (1 ≤ m < 100000) is the number of robot arms. The following m lines indicate the positions of the robot arms by two integers xi (0 < xi < 100000) and yi (1 ≤ yi < n). Here, xi is the x-coordinate of the i-th robot arm, which can pick goods on either the lane yi or the lane yi + 1 at position x = xi , and then release them on the other at the same x-coordinate. You can assume that positions of no two robot arms have the same x-coordinate, that is, xi ≠≠ xj for any i ≠≠ j

Output

Output n integers separated by a space in one line. The i-th integer is the number of the manufacturing lines from which the storage room connected to the conveyor lane i can accept goods.

Sample Input

4 3
1000 1
2000 2
3000 3

Sample Output

2 3 4 4

这个题目我觉得就是思维题，需要找规律，有两个小规律，一个就是两条生产线之间的物品可以交换，不过这个要按照x坐标排一下顺序，只有一部分可以交换，这个自己仔细读题吧。
还有就是无论哪条线它的物品的数值都是连续的，所以我们只要维护每一个位置的左右物品的数值就可以了。
这个规律我一直没有发现，因为我在写题的过程中默认把所有的物品当成一样的了，