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 <iostream>
#include <vector>
using namespace std;
typedef pair<int, int> P;

template <typename T>
struct Edge
{
    int to;
    T cost;
};

template <typename T>
struct WeightedGraph
{
    int n;
    vector<vector<Edge<T>>> g;
    
    WeightedGraph(int n) : n(n){
        g.resize(n);
    }
    
    void init(int n_){
        n = n_;
        g.resize(n_);
    }
    
    void add_edge(int from, int to, T cost){
        g[from].push_back((Edge<T>){to, cost});
    }
};

int main()
{
    int n, m;
    cin >> n >> m;
    int d[100002];
    P p[100002];
    for(int i = 0; i < n; i++){
        cin >> d[i];
        p[i] = P(d[i], i);
    }
    sort(p, p + n);
    WeightedGraph<int> g(n);
    for(int i = 0; i < m; i++){
        int u, v;
        cin >> u >> v;
        u--; v--;
        g.add_edge(u, v, i);
        g.add_edge(v, u, i);
    }
    char c[100002];
    for(int i = 0; i < n; i++) c[i] = 'N';
    int l[200002];
    for(int i = 0; i < n; i++){
        int u = p[i].second;
        int les = 1000000000;
        bool b = false, w = false;
        for(Edge<int> e : g.g[u]){
            int v = e.to;
            les = min(les, d[v]);
            if(c[v] == 'B') b = true;
            if(c[v] == 'W') w = true;
        }
        if(!b && !w && les > d[u]){
            cout << -1 << endl;
            return 0;
        }
        les = 1000000000;
        for(Edge<int> e : g.g[u]){
            int v = e.to;
            if(c[v] != 'N') les = min(les, d[v]);
        }
        if(!b && (!w || (w && les == d[u]))) c[u] = 'B';
        else c[u] = 'W';
        for(Edge<int> e : g.g[u]){
            int v = e.to;
            if(c[v] == 'N') continue;
            if(c[v] == c[u]) l[e.cost] = max(d[u] - d[v], 1);
            else l[e.cost] = d[u];
        }
    }
    for(int i = 0; i < n; i++) cout << c[i];
    cout << endl;
    for(int i = 0; i < m; i++) cout << l[i] << endl;
}