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;
typedef unsigned long long ull;
typedef pair<ll, ll> P;

#define fi first
#define se second
#define repl(i,a,b) for(ll i=(ll)(a);i<(ll)(b);i++)
#define rep(i,n) repl(i,0,n)
#define all(x) (x).begin(),(x).end()
#define dbg(x) cout<<#x"="<<x<<endl
#define mmax(x,y) (x>y?x:y)
#define mmin(x,y) (x<y?x:y)
#define maxch(x,y) x=mmax(x,y)
#define minch(x,y) x=mmin(x,y)
#define uni(x) x.erase(unique(all(x)),x.end())
#define exist(x,y) (find(all(x),y)!=x.end())
#define bcnt __builtin_popcountll

#define INF 1e16
#define mod 1000000007

struct edge{
	ll v,idx,w;
};

ll N,M;
vector<ll> D;
vector<edge> es[200010];
ll res[200010],resC[200010];
bool solved[200010];

int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);

  cin>>N>>M;
  D.resize(N);
  rep(i,N)cin>>D[i];
  rep(i,M){
  	ll u,v;
  	cin>>u>>v;
  	u--;v--;
  	if(D[u]<D[v]||(D[u]==D[v]&&u<v))swap(u,v);
  	es[u].push_back((edge){v,i,D[u]});
  	res[i]=D[u];
  }
  priority_queue<P,vector<P>,greater<P>> que;
  rep(i,N){
  	que.push(P(D[i],i));
  }
  while(que.size()){
  	P p=que.top(); que.pop();
  	ll v=p.se;
  	ll d=p.fi;
  	bool ok=true;
  	for(edge e : es[v]){
  		if(!solved[e.v]&&D[e.v]!=d){
  			ok=false;
  		}
  	}
  	if(!ok){
  		cout<<-1<<endl;
  		return 0;
  	}
  	if(es[v].size()==0){
  		continue;
  	}
  	bool col=false;
  	for(edge e : es[v]){
  		solved[e.v]=true;
  		if(resC[e.v]==0)col=true;
  	}
  	resC[v]=col;
  	solved[v]=true;
  }
  rep(i,N){
  	if(!solved[i]){
  		cout<<-1<<endl;
  		return 0;
  	}
  }
  rep(i,N){
  	if(resC[i]==0)cout<<"W";
  	else cout<<"B";
  }
  cout<<"\n";
  rep(i,M){
  	cout<<res[i]<<"\n";
  }

  return 0;
}