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 CPP):

Solution:
#include <algorithm>
#include <cstdio>
#include <string>
#include <vector>

using namespace std;

constexpr int kMaxC = 1000000000;

struct Edge
{
    int u, v, c;
};

struct Node
{
    int i, d;
    char color;
    vector<Edge*> edges;
};

bool operator<(const Node& u, const Node& v)
{
    if (u.d != v.d) return u.d < v.d;
    if (u.i != v.i) return u.i < v.i;
    return false;
}

int main()
{
    int n, m; scanf("%d%d", &n, &m);
    vector<Node> nodes(n);
    for (int i = 0; i < n; i++) {
        int d; scanf("%d", &d);
        nodes[i] = {i, d, '?', {}};
    }
    vector<Edge> edges(m);
    for (int i = 0; i < m; i++) {
        int u, v; scanf("%d%d", &u, &v);
        edges[i] = {--u, --v, kMaxC};
        nodes[u].edges.push_back(&edges[i]);
        nodes[v].edges.push_back(&edges[i]);
    }

    sort(nodes.begin(), nodes.end());

    vector<Node*> sedon(n);
    for (int i = 0; i < n; i++)
        sedon[nodes[i].i] = &nodes[i];
    
    for (Node& v : nodes) {
        if (v.color != '?') continue;

        for (Edge* e : v.edges) {
            int u_i = (e->u != v.i) ? e->u : e->v;
            Node& u = *sedon[u_i];
            if (u.d == v.d || u.color != '?') {
                v.color = (u.color == 'B') ? 'W' : 'B';
                u.color = (v.color == 'B') ? 'W' : 'B';
                e->c = v.d;
                break;
            }
        }
        if (v.color == '?') {
            puts("-1");
            return 0;
        }
    }

    for (const Node* v : sedon)
        putchar(v->color);
    putchar('\n');
    for (const Edge& e : edges)
        printf("%d\n", e.c);

    return 0;
}