Problem: We have a connected undirected graph with N vertices and M edges. Edge i in this graph (1 \leq i \leq M) connects Vertex U_i and Vertex V_i bidirectionally. We are additionally given N integers D_1, D_2, ..., D_N.

Determine whether the conditions below can be satisfied by assigning a color - white or black - to each vertex and an integer weight between 1 and 10^9 (inclusive) to each edge in this graph. If the answer is yes, find one such assignment of colors and integers, too.

* There is at least one vertex assigned white and at least one vertex assigned black.
* For each vertex v (1 \leq v \leq N), the following holds.
* The minimum cost to travel from Vertex v to a vertex whose color assigned is different from that of Vertex v by traversing the edges is equal to D_v.



Here, the cost of traversing the edges is the sum of the weights of the edges traversed.

Constraints

* 2 \leq N \leq 100,000
* 1 \leq M \leq 200,000
* 1 \leq D_i \leq 10^9
* 1 \leq U_i, V_i \leq N
* The given graph is connected and has no self-loops or multiple edges.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M
D_1 D_2 ... D_N
U_1 V_1
U_2 V_2
\vdots
U_M V_M


Output

If there is no assignment satisfying the conditions, print a single line containing `-1`.

If such an assignment exists, print one such assignment in the following format:


S
C_1
C_2
\vdots
C_M


Here,

* the first line should contain the string S of length N. Its i-th character (1 \leq i \leq N) should be `W` if Vertex i is assigned white and `B` if it is assigned black.
* The (i + 1)-th line (1 \leq i \leq M) should contain the integer weight C_i assigned to Edge i.

Examples

Input

5 5
3 4 3 5 7
1 2
1 3
3 2
4 2
4 5


Output

BWWBB
4
3
1
5
2


Input

5 7
1 2 3 4 5
1 2
1 3
1 4
2 3
2 5
3 5
4 5


Output

-1


Input

4 6
1 1 1 1
1 2
1 3
1 4
2 3
2 4
3 4


Output

BBBW
1
1
1
2
1
1

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class Main {
    static ArrayList<Edge>[] graph;
    public static void main(String[] args) {
        FastScanner scanner = new FastScanner();
        PrintWriter out = new PrintWriter(System.out,false);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        int[][] weights= new int[n][2];
        int[] unsorted = new int[n];
        int[] rev = new int[n];
        for(int i = 0; i < n; i++) {
            weights[i][0] = scanner.nextInt();
            weights[i][1] = i;
            unsorted[i] = weights[i][0];
        }
        Arrays.sort(weights, new Comparator<int[]>() {
            public int compare(int[] o1, int[] o2) {
                return o1[0] - o2[0];
            }
        });
        for(int i = 0; i < n; i++) {
            rev[weights[i][1]] = i;
        }
        Edge[] edges = new Edge[m];
        graph = new ArrayList[n];
        for(int i = 0; i < n; i++) {
            graph[i] = new ArrayList<>();
        }
        for(int i = 0; i < m; i++) {
            int u = scanner.nextInt()-1;
            int v = scanner.nextInt()-1;
            edges[i] = new Edge(u,v,i);
            graph[u].add(edges[i]);
            graph[v].add(edges[i]);
        }
        Boolean[] cols = new Boolean[n];
        //for(Edge edge: graph[weights[0][1]]) {
        //    int o = edge.u == weights[0][1] ? edge.v: edge.u;
        //    //System.out.println(o + " " + weights[0][1]);
        //    if (unsorted[o] == weights[0][0]) {
        //        cols[weights[0][1]] = true;
        //        cols[o] = false;
        //        //System.out.println(0);
        //        edge.w = weights[0][0];
        //        break;
        //    }
        //}
        //if (cols[weights[0][1]] == null) {
        //    System.out.println(-1);
        //    return;
        //}
top:
        for(int i = 0; i < n; i++) {
            //System.out.println(Arrays.toString(cols));
            int cur = weights[i][1];
            if (cols[cur]!=null)continue;
            int ww = weights[i][0];
            //System.out.println("cur: " + cur + " ww: " + ww);
            for(Edge edge: graph[cur]) {
                int o = edge.u == cur ? edge.v: edge.u;
               // System.out.println(edge.u + " " + edge.v);
                if (cols[o] != null) {
                    if (ww == unsorted[o]) {
                        cols[cur] = !cols[o];
                        edge.w = ww;
                    }
                    else {
                        cols[cur] = cols[o];
                        edge.w = ww - unsorted[o];
                    }
                    continue top;
                } else if (unsorted[o] == ww) {
                    cols[cur] = true;
                    cols[o] = false;
                    edge.w = ww;
                    continue top;
                }
            }
            System.out.println(-1);
            return;
        }
        //System.out.println(Arrays.toString(cols));
        for(int i = 0; i < n; i++) {
            out.print(cols[i] ? 'B' : 'W'); 
        }
        out.println();
        for(int i = 0; i < m; i++) {
            //out.print((edges[i].u+1) + " " + (edges[i].v+1) + " " );
            out.println(edges[i].w);
        }
        out.flush();
    }
    static class Edge {
        int u,v,ind,w;
        public Edge(int uu, int vv, int ii) {
            u = uu; v = vv; ind = ii;
            w = 1_000_000_000;
        }
    }
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }
        public FastScanner() {
            this(new InputStreamReader(System.in));
        }
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        String readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}