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;
#define pb push_back
#define fi first
#define se second
typedef pair<ll,ll> P;
using VP = vector<P>; using VVP = vector<VP>;
using VI = vector<ll>; using VVI = vector<VI>; using VVVI = vector<VVI>;
const int inf=1e9+7;
const ll INF=1LL<<61;
const ll mod=1e9+7;

int main(){
  int i,j;
  int n,m;
  cin>>n>>m;
  vector<P> d(n);
  VI dd(n);
  vector <vector<P> > E(n);
  VI c(n,0);
  VI h(m,-1);
  int x;
  for(i=0;i<n;i++) {
    cin>>x;
    d[i]=P(x,i);
    dd[i]=x;
  }
  sort(d.begin(),d.end());

  int u,v;
  for(i=0;i<m;i++){
    cin>>u>>v;
    u--; v--;
    E[u].pb(P(v,i));
    E[v].pb(P(u,i));
  }
  int te=1;

  for(i=0;i<n;i++){
    int s=d[i].se;
    bool ng=1;
    for(P t:E[s]){
      if(dd[t.fi]<=dd[s]){
        if(c[s]==0&&c[t.fi]==0) {
          c[t.fi]=-1;
          c[s]=-c[t.fi];
        }
        else if(c[s]==0&&c[t.fi]!=0) c[s]=-c[t.fi];
        h[t.se]=dd[s];
        ng=0;
      }
    }
    if(ng){
      cout<<-1<<endl;
      return 0;
    }
    
    //cout<<i<<" "<<c[i]<<endl;
  }

  for(i=0;i<n;i++){
    if(c[i]==-1) cout<<"B";
    else cout<<"W";
  }
  cout<<endl;
  for(i=0;i<m;i++){
    assert(h[i]!=-1);
    cout<<(int)h[i]<<endl;
  }

  return 0;
}