Lexical Sign Sequence

문제

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.

입력

Input begins with a line containing two integers: N K (1 ≤ N ≤ 100000; 0 ≤ K ≤ 100000) representing the length of the sequence and the number of constraints, respectively. The second line contains N integers: P_i (−1 ≤ P_i ≤ 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 ≤ A_i ≤ B_i ≤ N; −N ≤ C_i ≤ N) representing the i^th constraint.

출력

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.