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<bits/stdc++.h>
using namespace std;

const int N = 1e5+7, INF = 1e9;
int d[N];
int col[N];

struct Edge {
    int u, v, w;
    Edge(int u, int v) :u(u), v(v), w(INF) {}
    int other(int x) {return u^v^x;}
};

vector<int> adj[N];
vector<Edge> edges;

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);

    int n, m;
    cin>>n>>m;

    vector<int> order;

    for (int i=1; i<=n; i++)    {
        cin>>d[i];
        order.push_back(i);
    }

    auto comp = [](int x, int y) {return d[x] < d[y];};
    sort(order.begin(), order.end(), comp);

    for (int i=1; i<=m; i++) {
        int u, v;
        cin>>u>>v;
        edges.emplace_back(u, v);
        adj[u].push_back(edges.size()-1);
        adj[v].push_back(edges.size()-1);
    }

    for (int u: order) {
        if (col[u])    continue;
        bool found = false;
        for (int e: adj[u]) {
            int v = edges[e].other(u);
            if (col[v])  {
                edges[e].w = d[u];
                found = true;
                col[u] = 3 - col[v];
                break;
            }
        }

        if (!found) {
            for (int e: adj[u]) {
                int v = edges[e].other(u);
                if (d[v] == d[u]) {
                    edges[e].w = d[u];
                    found = true;
                    col[u] = 1;
                    col[v] = 2;
                    break;
                }
            }
        }
        if (!found) {
            cout<<-1<<endl;
            return 0;
        }
    }

    for (int i=1; i<=n; i++)
        if (col[i] == 1)    cout<<"W";
        else                cout<<"B";
    cout<<endl;
    for (int i=0; i<edges.size(); i++)  cout<<edges[i].w<<"\n";
}