A13566 | Graph Coloring

You are given an undirected graph without self-loops or multiple edges which consists of $n$ vertices and $m$ edges. Also you are given three integers $n_1$ , $n_2$ and $n_3$ .

Can you label each vertex with one of three numbers 1, 2 or 3 in such way, that:

1. Each vertex should be labeled by exactly one number 1, 2 or 3;
2. The total number of vertices with label 1 should be equal to $n_1$ ;
3. The total number of vertices with label 2 should be equal to $n_2$ ;
4. The total number of vertices with label 3 should be equal to $n_3$ ;
5. $|col_u - col_v| = 1$ for each edge $(u, v)$ , where $col_x$ is the label of vertex $x$ .

If there are multiple valid labelings, print any of them.

The first line contains two integers $n$ and $m$ ( $1 \le n \le 5000$ ; $0 \le m \le 10^5$ ) — the number of vertices and edges in the graph.

The second line contains three integers $n_1$ , $n_2$ and $n_3$ ( $0 \le n_1, n_2, n_3 \le n$ ) — the number of labels 1, 2 and 3, respectively. It's guaranteed that $n_1 + n_2 + n_3 = n$ .

Next $m$ lines contan description of edges: the $i$ -th line contains two integers $u_i$ , $v_i$ ( $1 \le u_i, v_i \le n$ ; $u_i \neq v_i$ ) — the vertices the $i$ -th edge connects. It's guaranteed that the graph doesn't contain self-loops or multiple edges.

If valid labeling exists then print "YES" (without quotes) in the first line. In the second line print string of length $n$ consisting of 1, 2 and 3. The $i$ -th letter should be equal to the label of the $i$ -th vertex.

If there is no valid labeling, print "NO" (without quotes).