G - 01Sequence

Score : $600$ points

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.

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.

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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.

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6 3
1 4 3
2 2 1
4 6 2

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.

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8 2
2 6 1
3 5 3

0 0 1 1 1 0 0 0