A13821 | Lookup Tables

The first line contains two integers $K$ and $Q$ ( $ 1 <= K <= 16$ , $1 <= Q <= 2\cdot 10^5$ ).

Each of the next $Q$ lines contains three integers $l_i$ , $r_i$ and $v_i$ . ( $0 \leq l_i \leq r_i < 2^{2K}$ , $0 \leq v_i < 2^{16}$ ).

On the first line output "possible" (without quotes) if two tables satisfying the conditions exist, or "impossible" (without quotes) if they don't exist.

If a solution exists, in the next $2 \cdot 2^K$ lines your program should output all values of the two lookup tables (LSBTable and MSBTable) it found. When there are multiple pairs of tables satisfying the conditions, your program may output any such pair.

On lines $1 + i$ output $\textrm{LSBTable}[i]$ . ( $0 \leq i < 2^K$ , $0 \leq \textrm{LSBTable}[i] < 2^{16}$ ).

On lines $1 + 2^K + i$ output $\textrm{MSBTable}[i]$ . ( $0 \leq i < 2^K$ , $0 \leq \textrm{MSBTable}[i] < 2^{16}$ ).

A closed interval $[a, b]$ includes both a and b.

In the first sample, tables $\textrm{LSBTable} = [1,3]$ and $\textrm{MSBTable} = [1,3]$ satisfy the conditions: $F[0] = \textrm{LSBTable}[0] \& \textrm{MSBTable}[0] = 1 \& 1 = 1$ , $F[1] = \textrm{LSBTable}[1] \& \textrm{MSBTable}[0] = 3 \& 1 = 1$ , $F[2] = \textrm{LSBTable}[0] \& \textrm{MSBTable}[1] = 1 \& 3 = 1$ , $F[3] = \textrm{LSBTable}[1] \& \textrm{MSBTable}[1] = 3 \& 3 = 3$ .

In the second sample, tables $\textrm{LSBTable} = [3,3,2,2]$ and $\textrm{MSBTable} = [0,3,0,1]$ satisfy all the conditions.

In the third sample there are no two lookup tables which can satisfy the conditions.