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<algorithm>
#define ep emplace
#define eb emplace_back
#define fi first
#define se second
#define all(x) (x).begin(),(x).end()
#define semicolon ;
#define ryan bear
using namespace std;
typedef long long ll;
typedef pair<int,int>pi;
typedef pair<ll,ll>pl;
const int inf=1e9+7;
const ll INF=1e18;
vector<pi>adj[100010];
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    int v,e;
    cin>>v>>e;
    vector<pi>p(v);
    vector<int>d(v);
    vector<int>cost(e,1000000000);
    for(int&t:d)
        cin>>t;
    for(int i=0;i<e;i++)
    {
        int u,v;
        cin>>u>>v;
        adj[--u].eb(--v,i);
        adj[v].eb(u,i);
    }
    for(int i=0;i<v;i++)
        p[i].fi=d[i],p[i].se=i;
    sort(all(p));
    vector<int>col(v,0);
    for(pi&tt:p)
    {
        int i=tt.se;
        if(col[i]!=0)
            continue;
        for(pi&t:adj[i])
        {
            if(d[t.fi]<=d[i])
            {
                if(col[t.fi]==0)
                    col[t.fi]=1;
                col[i]=col[t.fi]==1?2:1;
                cost[t.se]=d[i];
                break;
            }
        }
        if(col[i]==0)
            return cout<<-1<<endl,0;
    }
    for(int i=0;i<v;i++)
        cout<<(col[i]==1?'B':'W');
    for(int i=0;i<e;i++)
        cout<<'\n'<<cost[i];
    cout<<endl;
    return 0;
}