H. Lexical Sign Sequence
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Andi likes numbers and sequences, especially, sign sequences. A sign sequence is a sequence which consists of $$$-1$$$ and $$$1$$$. Andi is a curious person, thus, he wants to build a sign sequence which length is $$$N$$$ (the positions are numbered from $$$1$$$ to $$$N$$$, inclusive).

However, Andi also likes some challenges. Therefore, he prefilled some positions in the sequence with $$$-1$$$ or $$$1$$$ (the number in these positions cannot be changed). Andi also wants the sequence to fulfill $$$K$$$ constraints. For each constraint, there are 3 numbers: $$$A_i$$$, $$$B_i$$$, and $$$C_i$$$. This means that the sum of numbers which position is in the range $$$[A_i, B_i]$$$ (inclusive) must be at least $$$C_i$$$.

Sounds confusing, right? It is not done yet. Since there can be many sequences that fulfill all the criteria above, Andi wants the sequence to be lexicographically smallest. Sequence $$$X$$$ is lexicographically smaller than sequence $$$Y$$$ if and only if there exists a position $$$i$$$ where $$$X_i < Y_i$$$ and $$$X_j = Y_j$$$ for all $$$j < i$$$.

Find the sequence Andi wants.

Input

Input begins with a line containing two integers: $$$N$$$ $$$K$$$ ($$$1 \le N \le 100000$$$; $$$0 \le K \le 100000$$$) representing the length of the sequence and the number of constraints, respectively. The second line contains $$$N$$$ integers: $$$P_i$$$ ($$$-1 \le P_i \le 1$$$). If $$$P_i = 0$$$, then the $$$i^{th}$$$ position in the sequence is not prefilled, otherwise the $$$i^{th}$$$ position in the sequence is prefilled by $$$P_i$$$. The next $$$K$$$ lines, each contains three integers: $$$A_i$$$ $$$B_i$$$ $$$C_i$$$ ($$$1 \le A_i \le B_i \le N$$$; $$$-N \le C_i \le N$$$) representing the $$$i^{th}$$$ constraint.

Output

Output contains $$$N$$$ integers (each separated by a single space) in a line representing the sequence that Andi wants if there exists such sequence, or "Impossible" (without quotes) otherwise.

Examples
Input
3 2
0 0 0
1 2 2
2 3 -1
Output
1 1 -1
Input
3 2
0 -1 0
1 2 2
2 3 -1
Output
Impossible
Note

Explanation for the sample input/output #1

Both sequences $$$[1, 1, -1]$$$ and $$$[1, 1, 1]$$$ satisfy the prefilled conditions and the given $$$K$$$ constraints. The former is lexicographically smaller.

Explanation for the sample input/output #2

The second position is already prefilled with $$$-1$$$, so it is impossible to fulfill the first constraint. There is no valid sequence in this case.