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<algorithm>
#include<vector>
#include<queue>
#include<string>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> P;
#define int ll
ll v_color[200005]={0};
vector<P> knode[200005],node[200005];
const ll inf=1e9;
ll ans[200005]={0};
ll dn[200005]={0};
void dfs(ll pos,ll val){
  v_color[pos]=val;
  for(int i=0;i<node[pos].size();i++){
    ll to=node[pos][i].first;
    if(v_color[to]==0){
      ans[node[pos][i].second]=dn[to];
      dfs(to,val%2+1);
    }
  }
}
signed main(){
  ll n,m;
  cin>>n>>m;
  vector<P> vec;
  for(int i=1;i<=n;i++){
    ll val;
    cin>>val;
    dn[i]=val;
    vec.push_back(P(val,i));
  }
  sort(vec.begin(),vec.end());
  for(int i=1;i<=m;i++){
    ll u,v;
    cin>>u>>v;
    knode[u].push_back(P(v,i));
    knode[v].push_back(P(u,i));
  }
  for(int i=1;i<=n;i++){
    P min_v=P(inf,inf);
    for(int j=0;j<knode[i].size();j++){
      ll to=knode[i][j].first;
      min_v=min(min_v,P(dn[to],j));
    }
    node[i].push_back(knode[i][min_v.second]);
    node[knode[i][min_v.second].first].push_back(P(i,knode[i][min_v.second].second));
  }
  for(int i=1;i<=n;i++){
    bool f=false;
    for(int j=0;j<knode[i].size();j++){
      ll to=knode[i][j].first;
      if(dn[to]<=dn[i]) f=true;
    }
    if(!f){
      cout<<-1<<endl;
      return 0;
    }
  }
  for(int i=0;i<n;i++){
    ll pos=vec[i].second;
    if(v_color[pos]==0){
      dfs(pos,1);
    }
  }
  for(int i=1;i<=n;i++) {
    if(v_color[i]==0) cout<<"0";
    else if(v_color[i]==1) cout<<"B";
    else cout<<"W";
  }
  cout<<endl;
  for(int i=1;i<=m;i++){
    cout<<(ans[i]==0?inf:ans[i])<<endl;
  }
}