Problem Statement

You are given Q triples of integers $(a_1, b_1, d_1), (a_2, b_2, d_2), \ldots, (a_Q, b_Q, d_Q)$.
A subset S of the set $\lbrace 1, 2, \ldots, Q\rbrace$ is defined to be a good set if there exists an integer sequence $(X_1, X_2, \ldots, X_N)$ of length N that satisfies:

X_{a_i} - X_{b_i} = d_i for all $i \in$ S.

Starting with S as an empty set, perform the following operation for $i = 1, 2, \ldots, Q$ in this order:

If $S \cup \lbrace i \rbrace$ is a good set, then replace S with $S \cup \lbrace i \rbrace$.

Print all elements of the final set S in ascending order.

Input

The input is given from Standard Input in the following format:
N Q
a_1 b_1 d_1
a_2 b_2 d_2
$\vdots$
a_Q b_Q d_Q

Output

Print the sequence $(s_1, s_2, \ldots, s_k)$ of all elements of the final set S in ascending order, separated by spaces, in the following format:
$s_1 s_2 \ldots s_k$

Constraints

• All input values are integers.
• $1 \leq N, Q \leq 2 \times 10^5$
• $1 \leq a_i, b_i \leq N$
• -$10^9 \leq d_i \leq 10^9$

Sample Input 1

3 5
1 2 2
3 2 -3
2 1 -1
3 3 0
1 3 5

Sample Output 1

1 2 4 5

Starting with S as an empty set, perform the operation described in the problem statement for i = 1, 2, 3, 4, 5 in this order, as follows.

• For i = 1, the set $S \cup \lbrace i \rbrace = \lbrace 1 \rbrace$ is a good set, because (X_1, X_2, X_3) = (3, 1, 4) satisfies the condition in the problem statement, for example, so replace S with $\lbrace 1\rbrace$.
• For i = 2, the set $S \cup \lbrace i \rbrace = \lbrace 1, 2 \rbrace$ is a good set, because (X_1, X_2, X_3) = (3, 1, -2) satisfies the condition in the problem statement, for example, so replace S with $\lbrace 1, 2\rbrace$.
• For i = 3, the set $S \cup \lbrace i \rbrace = \lbrace 1, 2, 3 \rbrace$ is not a good set.
• For i = 4, the set $S \cup \lbrace i \rbrace = \lbrace 1, 2, 4 \rbrace$ is a good set, because (X_1, X_2, X_3) = (3, 1, -2) satisfies the condition in the problem statement, for example, so replace S with $\lbrace 1, 2, 4\rbrace$.
• For i = 5, the set $S \cup \lbrace i \rbrace = \lbrace 1, 2, 4, 5 \rbrace$ is a good set, because (X_1, X_2, X_3) = (3, 1, -2) satisfies the condition in the problem statement, for example, so replace S with $\lbrace 1, 2, 4, 5\rbrace$.

Therefore, the final set S is $\lbrace 1, 2, 4, 5\rbrace$.

Sample Input 2

200000 1
1 1 1

Sample Output 2

The final set S is empty.

Sample Input 3

5 20
4 2 125421359
2 5 -191096267
3 4 -42422908
3 5 -180492387
3 3 174861038
2 3 -82998451
3 4 -134761089
3 1 -57159320
5 2 191096267
2 4 -120557647
4 2 125421359
2 3 142216401
4 5 -96172984
3 5 -108097816
1 5 -50938496
1 2 140157771
5 4 65674908
4 3 35196193
4 4 0
3 4 188711840

Sample Output 3

1 2 3 6 8 9 11 14 15 16 17 19

见题面 Input 部分

见题面 Output 部分