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;

int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    
    int n, m;
    static pair<int64_t, int> weight[100000];
    static int w[100000];
    static char color[100001];
    static int ans[200000];
    static vector<tuple<int64_t, int, int>> edges[100000];
    cin >> n >> m;
    for(int i=0;i<n;++i){
        int d;
        cin >> d;
        weight[i] = {d, i};
        w[i] = d;
    }
    for(int i=0;i<m;++i){
        int u, v;
        cin >> u >> v;
        --u; --v;
        edges[u].emplace_back(weight[v].first, v, i);
        edges[v].emplace_back(weight[u].first, u, i);
    }
    sort(weight, weight + n);
    for(int i=0;i<n;++i) sort(edges[i].begin(), edges[i].end());

    for(int i=0;i<n;++i){
        int v = weight[i].second, to = get<1>(edges[v][0]), e = get<2>(edges[v][0]);
        if(color[v] != 0) continue;
        if(color[to] != 0){
            color[v] = 'W' + 'B' - color[to];
            ans[e] = w[v];
        }else{
            cerr << to << " " << v << endl;
            if(w[to] != w[v]){ cout << -1 << endl; return 0; }
            color[v] = 'W'; color[to] = 'B';
            ans[e] = w[v];
        }
    }
    cout << color << endl;
    for(int i=0;i<m;++i) cout << (ans[i] == 0 ? 1000000000 : ans[i]) << endl;

    return 0;
}