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 MX=2e5+5;
int d[MX];
pair<int,int> e[MX];
char c[MX];
const int INF=1e9;
int b[MX];
int n,m;
vector<pair<int,int>> a[MX];
int main(){
    cin.tie(0);
    ios_base::sync_with_stdio(0);
    cin>>n>>m;
    int i;
    for(i=1 ; i<=m ;i++)b[i]=INF;
    for(i=1 ; i<=n ; i++)cin>>d[i],e[i]={d[i],i};
    for(i=1 ; i<=m ; i++){
        int u,v;
        cin>>u>>v;
        a[u].push_back({v,i});
        a[v].push_back({u,i});
    }

    sort(e+1,e+n+1);
    for(i=1 ; i<=n ; i++){
        int v=e[i].second;
        if(c[v])continue;
        for(auto j: a[v]){
            int u=j.first;
            if(d[u]<d[v]){
                if(c[u]=='B')c[v]='W';
                else c[v]='B';
                b[j.second]=d[v];
                break;
            }
            if(d[u]==d[v]){
                if(c[u]=='B')c[v]='W';
                else{
                    c[v]='B';
                    c[u]='W';
                }
                b[j.second]=d[v];
                break;
            }
        }
       // cout<<v<<" "<<c[v]<<endl;
    }
    int isok=1;

    for(i=1 ; i<=n ; i++){
       // cout<<c[i]<<endl;
        if(c[i]==0)isok=0;
    }
    if(isok==0){
        cout<<-1;
        return 0;
    }

    cout<<c+1<<endl;
    for(i=1 ; i<=m ; i++){
        cout<<b[i]<<"\n";
    }
    return 0;
}