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;
typedef long long ll;

signed main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);

    int n,m;
    cin>>n>>m;
    array<int,2> d[n];
    int a[n];
    for(int i=0;i<n;i++){
        cin>>a[i];
        d[i] = {a[i],i};
    }
    sort(d,d+n);
    vector<vector<array<int,2>>> v(n);
    for(int i=0;i<m;i++){
        int a,b;
        cin>>a>>b;
        a--,b--;
        v[a].push_back({b,i});
        v[b].push_back({a,i});
    }
    int c[n];
    for(int i=0;i<n;i++) c[i] = -1;
    int ans[m];
    int INF = 1e9;
    for(int i=0;i<m;i++) ans[i] = INF;
    priority_queue<array<int,2>,vector<array<int,2>>,greater<array<int,2>>> q;
    q.push({d[0][0],d[0][1]});
    bool used[n];
    for(int i=0;i<n;i++) used[i] = 0;
    while(q.size()){
        array<int,2> p = q.top();
        //cerr << p[0] << " " << p[1] << endl;
        q.pop();
        used[p[1]]=1;
        if(c[p[1]]==-1) c[p[1]] = 1;
        for(auto i:v[p[1]]){
            if(c[i[0]]==-1) c[i[0]] = c[p[1]] ^ 1;
            ans[i[1]] = max(a[i[0]], p[0]);
            if(!used[i[0]]){
                used[i[0]]=1;
                q.push({a[i[0]],i[0]});
            }
        }
    }
    for(int i=0;i<n;i++){
        bool pos = false;
        for(auto j:v[i]){
            int p = j[0];
            int itr = j[1];
            if(c[p] == c[i]) continue;
            if(ans[itr] < a[i]){
                cout << -1 << endl;
                return 0;
            }
            if(ans[itr] == a[i]) pos = 1;
        }
        if(!pos){
            cout << -1 << endl;
            return 0;
        }
    }
    for(int i=0;i<n;i++){
        if(c[i] == 1) cout << "W";
        else cout << "B";
    }
    cout << "\n";
    for(int i=0;i<m;i++){
        cout << ans[i] << "\n";
    }
}