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;
using Int = long long;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}


template<typename T> void drop(const T &x){cout<<x<<endl;exit(0);}

//INSERT ABOVE HERE
signed main(){
  Int n,m;
  cin>>n>>m;
  vector<Int> ds(n);
  for(Int i=0;i<n;i++) cin>>ds[i];
  using P = pair<Int, Int>;
  map<P, Int> idx;
  vector< vector<Int> > G(n);
  for(Int i=0;i<m;i++){
    Int u,v;
    cin>>u>>v;
    u--;v--;
    idx[minmax({u,v})]=i;
    G[u].emplace_back(v);
    G[v].emplace_back(u);
  }

  vector<P> vp;
  for(Int i=0;i<n;i++)
    vp.emplace_back(ds[i],i);
  sort(vp.begin(),vp.end());

  const Int INF = 1e9;
  vector<Int> cs(n,-1);
  vector<Int> ans(m,INF);

  // same value
  for(auto p:vp){
    Int v=p.second;
    for(Int u:G[v]){
      if(~cs[u]) continue;
      if(ds[u]==ds[v]){
        if(cs[v]<0) cs[v]=0;
        cs[u]=!cs[v];
        ans[idx[minmax({u,v})]]=ds[v];
      }
    }
  }

  // other value
  for(auto p:vp){
    Int v=p.second;
    if(~cs[v]) continue;
    for(Int u:G[v]){
      if(ds[u]>ds[v]) continue;
      assert(ds[u]<ds[v]);
      assert(~cs[u]);
      cs[v]=!cs[u];
      ans[idx[minmax({u,v})]]=ds[v];
      break;
    }
    if(cs[v]<0) drop(-1);
  }

  for(Int i=0;i<n;i++) cout<<"BW"[cs[i]];
  cout<<endl;
  for(Int i=0;i<m;i++) cout<<ans[i]<<endl;
  return 0;
}