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 <iostream>
#include <vector>
#include <string>
#include <algorithm>

using namespace std;

class Node {
public:
    explicit Node(int dst = 0, int idx = -1) : dst(dst), idx(idx) {}
    int dst, idx;
};

int main(){
    int N, M;
    while(cin >> N >> M){
        vector<vector<Node>> g(N);
        vector<int> D(N);
        for(auto& t : D) cin >> t;
        vector<pair<int,int>> d;
        for(int i=0;i<N;i++){
            d.emplace_back(D[i], i);
        }
        for(int i=0;i<M;i++){
            int U, V; cin >> U >> V;
            --U; --V;
            g[U].emplace_back(V, i);
            g[V].emplace_back(U, i);
        }
        sort(d.begin(), d.end());
        string res(N, '?');
        vector<long long> cost(M, -1);
        vector<int> state(N, 0);
        for(int i=0;i<N;i++){
            for(auto& e : g[d[i].second]){
                if(res[d[i].second] != '?') break;
                int pos = e.dst;
                if(D[pos] < d[i].first){
                    if(res[pos] != '?'){
                        res[d[i].second] = res[pos];
                        cost[e.idx] = d[i].first - D[pos];
                    }
                } else if(D[pos] == d[i].first){
                    cost[e.idx] = D[pos];
                    if(res[pos] != '?'){
                        res[d[i].second] = (res[pos] == 'W' ? 'B' : 'W');
                    } else {
                        res[d[i].second] = 'W';
                        res[pos] = 'B';
                    }
                }
            }
        }
        if(res.find('?') == string::npos){
            cout << res << endl;
            for(auto& t : cost) cout << (t == -1 ? 1000000000 : t) << endl;
        } else {
            cout << -1 << endl;
        }
    }
}