Addition on Segments

Description:

Input:

The first line contains two integers $$$n$$$ and $$$q$$$ ($$$1 \leq n, q \leq 10^{4}$$$) — the length of the array and the number of queries in the initial problem.

The following $$$q$$$ lines contain queries, one per line. The $$$i$$$-th of these lines contains three integers $$$l_i$$$, $$$r_i$$$ and $$$x_i$$$ ($$$1 \leq l_i \leq r_i \leq n$$$, $$$1 \leq x_i \leq n$$$), denoting a query of adding $$$x_i$$$ to the segment from $$$l_i$$$-th to $$$r_i$$$-th elements of the array, inclusive.

Output:

In the first line print the only integer $$$k$$$, denoting the number of integers from $$$1$$$ to $$$n$$$, inclusive, that can be equal to the maximum in the array after applying some subset (possibly empty) of the given operations.

In the next line print these $$$k$$$ integers from $$$1$$$ to $$$n$$$ — the possible values of the maximum. Print these integers in increasing order.

Sample Input:

4 3
1 3 1
2 4 2
3 4 4

Sample Output:

4
1 2 3 4 

Sample Input:

7 2
1 5 1
3 7 2

Sample Output:

3
1 2 3 

Sample Input:

10 3
1 1 2
1 1 3
1 1 6

Sample Output:

6
2 3 5 6 8 9 

Note:

Consider the first example. If you consider the subset only of the first query, the maximum is equal to $$$1$$$. If you take only the second query, the maximum equals to $$$2$$$. If you take the first two queries, the maximum becomes $$$3$$$. If you take only the fourth query, the maximum becomes $$$4$$$. If you take the fourth query and something more, the maximum becomes greater that $$$n$$$, so you shouldn't print it.

In the second example you can take the first query to obtain $$$1$$$. You can take only the second query to obtain $$$2$$$. You can take all queries to obtain $$$3$$$.

In the third example you can obtain the following maximums:

• You can achieve the maximim of $$$2$$$ by using queries: $$$(1)$$$.
• You can achieve the maximim of $$$3$$$ by using queries: $$$(2)$$$.
• You can achieve the maximim of $$$5$$$ by using queries: $$$(1, 2)$$$.
• You can achieve the maximim of $$$6$$$ by using queries: $$$(3)$$$.
• You can achieve the maximim of $$$8$$$ by using queries: $$$(1, 3)$$$.
• You can achieve the maximim of $$$9$$$ by using queries: $$$(2, 3)$$$.