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<queue>
using namespace std;
struct node
{
	long long v,nxt,data;
	bool can;
};
node edge[1000001];
bool cn;
long long fa[1000001],FA[1000001],x,y,n,m,head[1000001],len,depth[1000001],d[1000001],D[1000001],RD[1000001],minnD[1000001];
void add(int x,int y,int z)
{
	edge[++len].v=y;
	edge[len].data=z;
	edge[len].nxt=head[x];
	head[x]=len;
	return;
}
void bfs(int x)
{
	int top;
	depth[x]=1;
	queue<int>q;
	q.push(x);
	while (!q.empty())
	{
		top=q.front();
		q.pop();
		for (int i=head[top];i>0;i=edge[i].nxt)
			if (!depth[edge[i].v]&&edge[i].can)
			{
				depth[edge[i].v]=depth[top]+1;
				FA[i]=top;
				fa[edge[i].v]=i;
				q.push(edge[i].v);
			}
	}
	return;
}
int main()
{
	len=1;
	cin>>n>>m;
	for (int i=1;i<=n;++i)
		cin>>D[i];
	for (int i=1;i<=m;++i)
	{
		cin>>x>>y;
		add(x,y,i);
		add(y,x,i);
	}
	for (int i=1;i<=n;++i)
	{
		minnD[i]=1e9;
		for (int j=head[i];j>0;j=edge[j].nxt)
			minnD[i]=min(minnD[i],D[edge[j].v]);
		cn=0;
		for (int j=head[i];j>0;j=edge[j].nxt)
			{
				if (cn==0&&minnD[i]==D[edge[j].v])
				{
					cn=1;
					edge[j].can=1;
					edge[j^1].can=1;
				}
			}
	}
	for (int i=1;i<=n;++i)
		if (!depth[i]) 
			bfs(i); 
	for (int i=1;i<=n;++i)
	{
		RD[i]=1e9;
		if (D[i]<D[FA[fa[i]]])
			d[edge[fa[i]].data]=D[FA[fa[i]]];
		else
			d[edge[fa[i]].data]=D[i];
	}
	for (int i=1;i<=n;++i)
		for (int j=head[i];j>0;j=edge[j].nxt)
			if (d[edge[j].data]!=0)
				RD[i]=min(RD[i],d[edge[j].data]);
	for (int i=1;i<=n;++i)
		if (RD[i]!=D[i])
		{
			cout<<-1<<endl;
			return 0;
		}
	for (int i=1;i<=n;++i)
		{
			if (depth[i]%2==0)
				cout<<'B';
			else
				cout<<'W'; 
		}
	cout<<endl;
	for (int i=1;i<=m;++i)
		{
			if (d[i]==0)
				cout<<1000000000<<endl;
			else
				cout<<d[i]<<endl;
		}
	return 0; 
}