write a go solution for Description:
You are given a graph consisting of n vertices and m directed arcs. The i-th arc goes from the vertex x_i to the vertex y_i, has capacity c_i and weight w_i. No arc goes into the vertex 1, and no arc goes from the vertex n. There are no cycles of negative weight in the graph (it is impossible to travel from any vertex to itself in such a way that the total weight of all arcs you go through is negative).

You have to assign each arc a flow (an integer between 0 and its capacity, inclusive). For every vertex except 1 and n, the total flow on the arcs going to this vertex must be equal to the total flow on the arcs going from that vertex. Let the flow on the i-th arc be f_i, then the cost of the flow is equal to sumlimits_i=1^mf_iw_i. You have to find a flow which minimizes the cost.

Sounds classical, right? Well, we have some additional constraints on the flow on every edge:

- if c_i is even, f_i must be even;
- if c_i is odd, f_i must be odd.

Can you solve this problem?

Input Format:
The first line contains two integers n and m (2<=n<=100; 1<=m<=200).

Then m lines follow. The i-th of them contains four integers x_i, y_i, c_i, and w_i (1<=x_i<=n-1; 2<=y_i<=n; x_iney_i; 1<=c_i<=100; -100<=w_i<=100). These integers describe the i-th arc.

Additional constraints on the input:

- there are no negative cycles in the graph.

Output Format:
If a flow satisfying all of the constraints does not exist, print Impossible.

Otherwise, print two lines:

- the first line should contain one word Possible;
- the second line should contain m integers f_1,f_2,...,f_m.

If there are multiple answers, print any of them. Note that the cost of the flow should be minimized.

Note:
None. Output only the code with no comments, explanation, or additional text.