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.*;

public class Main {
    public static final int MAX_WEIGHT = 1_000_000_000;

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        int[] d = new int[n];
        int[] toMin = new int[n];
        int[] curMin = new int[n];
        int[] edgeMin = new int[n];
        Arrays.fill(curMin, Integer.MAX_VALUE);

        for (int i = 0; i < n; i++) {
            d[i] = scanner.nextInt();
        }

        int u, v;
        for (int i = 0; i < m; i++) {
            u = scanner.nextInt()-1;
            v = scanner.nextInt()-1;
            if(curMin[u]>d[v]){
                toMin[u] = v;
                curMin[u] = d[v];
                edgeMin[u] = i;
            }
            if(curMin[v]>d[u]){
                toMin[v] = u;
                curMin[v] = d[u];
                edgeMin[v] = i;
            }
        }

        for (int i = 0; i < n; i++) {
            if(d[i]<curMin[i]){
                System.out.println(-1);
                return;
            }
        }


        int n1 = toMin.length;
        Boolean[] nodeColors = new Boolean[n1];
        Integer[] edgeWeights = new Integer[m];
        Stack<Integer> stack = new Stack<>();

        for (int i = 0; i < n1; i++) {
            if(nodeColors[i]!=null) continue;
            stack.push(i);
            while (!stack.isEmpty()){
                Integer peeked = stack.peek();
                if(nodeColors[toMin[peeked]]!=null){
                    nodeColors[peeked]=!nodeColors[toMin[peeked]];
                    edgeWeights[edgeMin[peeked]] = d[peeked];
                    stack.pop();
                }else{
                    if(d[toMin[peeked]]== d[peeked]){
                        toMin[toMin[peeked]] = peeked;
                        nodeColors[toMin[peeked]] = true;
                        nodeColors[peeked] = false;
                        edgeWeights[edgeMin[peeked]] = d[peeked];
                        stack.pop();
                    }else{
                        stack.push(toMin[peeked]);
                    }
                }
            }
        }

        for (int i = 0; i < edgeWeights.length; i++) {
            if (edgeWeights[i] == null) edgeWeights[i] = MAX_WEIGHT;
        }

        for (boolean color: nodeColors) {
            System.out.print(color ? "B" : "W");
        }
        System.out.println();
        for (int w : edgeWeights) {
            System.out.println(w);
        }
    }
}