Problem Statement

Consider a sequence of length N consisting of 0s and $1s, A=(A_1,A_2,\dots,A_N)$, that satisfies the following condition.

For every $i=1,2,\dots,M,$ there are at least X_i occurrences of $1 among A_{L_i}, A_{L_i+1}, \dots, A_{R_i}$.

Print one such sequence with the fewest number of occurrences of 1s.
There always exists a sequence that satisfies the condition under the Constraints.

Input

Input is given from Standard Input in the following format:
N M
L_1 R_1 X_1
L_2 R_2 X_2
$\vdots$
L_M R_M X_M

Output

Print a sequence A consisting of 0s and 1s, with spaces in between.
$A_1 A_2 \dots A_N$

It must satisfy all the requirements above.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq M \leq \min(2 \times 10^5, \frac{N(N+1)}{2} )$
• $1 \leq L_i \leq R_i \leq N$
• $1 \leq X_i \leq R_i-L_i+1$
• $(L_i,R_i) \neq (L_j,R_j)$ if $i \neq j$.
• All values in input are integers.

Sample Input 1

6 3
1 4 3
2 2 1
4 6 2

Sample Output 1

0 1 1 1 0 1

Another acceptable output is 1 1 0 1 1 0.
On the other hand, 0 1 1 1 1 1, which has more than the fewest number of 1s, is unacceptable.

Sample Input 2

8 2
2 6 1
3 5 3

Sample Output 2

0 0 1 1 1 0 0 0

见题面 Input 部分

见题面 Output 部分