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<iostream>
#include<vector>
#include<map>
#include<algorithm>
using namespace std;
int N,M;
int D[1<<17];
map<pair<int,int>,int>E;
vector<pair<int,int> >edges;
vector<int>G[1<<17];
int color[1<<17];
int main()
{
	cin>>N>>M;
	vector<pair<int,int> >d(N);
	for(int i=0;i<N;i++)
	{
		cin>>D[i];
		d[i]=make_pair(D[i],i);
	}
	for(int i=0;i<M;i++)
	{
		int u,v;cin>>u>>v;
		u--,v--;
		edges.push_back(minmax(u,v));
		G[u].push_back(v);
		G[v].push_back(u);
	}
	sort(d.begin(),d.end());
	for(int i=0;i<N;i++)
	{
		int u=d[i].second;
		for(int v:G[u])
		{
			if(D[v]<=D[u])
			{
				if(!color[u]&&color[v])
				{
					color[u]=3-color[v];
				}
				else if(!color[u]&&!color[v]&&D[u]==D[v])
				{
					color[u]=1;
					color[v]=2;
				}
				E[minmax(u,v)]=D[u];
			}
		}
		if(!color[u])
		{
			cout<<-1<<endl;
			return 0;
		}
	}
	for(int i=0;i<N;i++)cout<<(color[i]==1?'W':'B');
	cout<<endl;
	for(pair<int,int>p:edges)cout<<E[p]<<endl;
}