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;
template<typename T>
void fin(T a){
  cout<<a<<endl;
  exit(0);
}
const int INF=1e9;
template<typename T>
void chmin(T &a,T b){
  if(a>b)a=b;
}
typedef pair<int,int> P;

signed main(){
  int n,m;cin>>n>>m;
  vector<int> d(n),u(m),v(m);
  for(int i=0;i<n;i++)cin>>d[i];
  for(int i=0;i<m;i++){
    cin>>u[i]>>v[i];
    u[i]--;v[i]--;
  }
  vector<int> edge[n];
  for(int i=0;i<m;i++){
    edge[u[i]].push_back(v[i]);
    edge[v[i]].push_back(u[i]);
  }
  for(int i=0;i<n;i++){
    int A=INF;
    for(int p:edge[i])chmin(A,d[p]);
    if(A>d[i])fin(-1);
  }
  set<P> s;
  vector<int> edge2[n];
  map<P,int> ma;
  for(int i=0;i<n;i++){
    int idx,D=INF+1;
    for(int p:edge[i])if(D>d[p])D=d[p],idx=p;
    int A=idx,B=i;
    if(A>B)swap(A,B);
    if(s.count(P(A,B)))continue;
    s.insert(P(A,B));
    edge2[A].push_back(B);
    edge2[B].push_back(A);
    ma[P(A,B)]=d[i];
  }
  vector<int> col(n,0);
  queue<int> que;
  for(int i=0;i<n;i++){
    if(col[i])continue;
    col[i]=1;
    que.push(i);
    while(que.size()){
      int p=que.front();que.pop();
      for(int q:edge2[p]){
        if(col[q])continue;
        col[q]=-col[p];
        que.push(q);
      }
    }
  }
  for(int i=0;i<n;i++)cout<<(~col[i]?'B':'W');cout<<endl;
  for(int i=0;i<m;i++){
    if(u[i]>v[i])swap(u[i],v[i]);
    cout<<(ma[P(u[i],v[i])]?ma[P(u[i],v[i])]:INF)<<endl;
  }
}