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;
const int N=1e5+2;
const int M=2e5+2;
int ar[N],val[M],lis[N],color[N];
vector<pair<int,int> > adj[N];
signed main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	int n,i,j,k,l,m,v;
	cin>>n>>m;
	for(i=1;i<=n;i++){
		cin>>ar[i];
		lis[i]=i;
		color[i]=-1;
	}
	for(i=1;i<=m;i++){
		cin>>j>>k;
		adj[j].push_back({k,i});
		adj[k].push_back({j,i});
	}
	sort(lis+1,lis+1+n,[&](int x,int y){
		return ar[x]<ar[y];	
	});
	for(i=1;i<=n;i++){
		v=lis[i];
		if(color[v]!=-1){
			continue;
		}
		bool cac=true;
		for(auto x:adj[v]){
			j=x.first; k=x.second;
			if(ar[v]>=ar[j]){
				if(color[j]!=-1){
					color[v]=1-color[j];
				}
				else{
					color[v]=0;
					color[j]=1;
				}
				val[k]=ar[v];
				cac=false;
				break;
			}
		}
		if(cac){
			cout<<-1;
			return 0;
		}
	}
	for(i=1;i<=n;i++){
		if(!color[i]){
			cout<<'B';
		}
		else{
			cout<<'W';
		}
	}
	cout<<'\n';
	for(i=1;i<=m;i++){
		if(!val[i]){
			val[i]=1000000000;
		}
		cout<<val[i]<<'\n';
	}
}