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<tuple>
#include<map>
#include<algorithm> // sort,reverse,min,lower_bound
#include<vector>
#include<iostream>
using namespace std;
#define df 0
#define INF 1000000000
#define rep(i,n) for(int i=0;i<(n);i++)
#define repa(i,a,n) for(int i=(a);i<(n);i++)
typedef long int li;

int main(){
  if(df) printf("*debug mode*\n");
  int n,m; cin >>n >>m;
  vector<pair<int,int>> d(n);
  rep(i,n){
    int x; cin >>x;
    d.at(i)=make_pair(x,i);
  }
  vector<vector<int>> adj(n);
  map<pair<int,int>,int> edge;
  rep(i,m){
    int u,v; cin >>u >>v; u--; v--;
    if(u>v)swap(u,v);
    edge[make_pair(u,v)]=i;
    adj.at(u).push_back(v);
    adj.at(v).push_back(u);
  }
  vector<int> col(n,-1),to(n,-1),w(m,INF);
  rep(i,n){
    if(to.at(i)!=-1)continue;
    for(int u:adj.at(i)){
      if(d.at(u).first>d.at(i).first) continue;
      to.at(i)=u;
      if(d.at(u).first==d.at(i).first){
	to.at(u)=i;
	if(col.at(u)==-1){
	  col.at(i)=0;
	  col.at(u)=1;
	}else{
	  col.at(i)=1-col.at(u);
	}
	if(df)printf("%d:0,%d:1\n",u,i);
	int j;
	if(u<i) j=edge[make_pair(u,i)];
	else  j=edge[make_pair(i,u)];
	w.at(j)=d.at(u).first;
      }
      break;
    }
    if(to.at(i)==-1){
      printf("-1");
      return 0;
    }
  }
  sort(d.begin(),d.end());
  if(df){
    for(auto x:d)printf("(%d,%d)",x.first,x.second);
    printf("\n");
  }
  rep(i,n){
    int u=d.at(i).second;
    if(col.at(u)!=-1)continue;
    int v=to.at(u);
    if(df)printf("%d->%d",u,v);
    col.at(u)=1-col.at(v);
    int j;
    if(u<v) j=edge[make_pair(u,v)];
    else  j=edge[make_pair(v,u)];
    w.at(j)=d.at(i).first;
    if(df)printf("%d\n",w.at(j));
  }
  rep(i,n) printf("%c",col.at(i)?'B':'W');
  printf("\n");
  rep(i,m){
    printf("%d\n",w.at(i));
  }
}

/// confirm df==0 ///