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 maxn=110000;
const int maxm=210000;
const int inf=1e9+7;
struct edge
{
	int to,nxt;
}e[maxm];
int h[maxn],E;
int n,m;
int d[maxn];
int w[maxm];
int use[maxn];
int col[maxn];
int root[maxn];
int fa[maxn];
int find(int x)
{
	if(fa[x]==x) return x;
	fa[x]=find(fa[x]);
	return fa[x];
}
void add(int u,int v)
{
	E++;
	e[E].to=v;
	e[E].nxt=h[u];
	h[u]=E;
	return;
}
void mer(int u,int v)
{
	u=find(u);
	v=find(v);
	if(u==v) return;
	fa[u]=v;
}
void dfs(int u,int fa)
{
	col[u]=col[fa]^1;
	for(int i=h[u];i;i=e[i].nxt)
	{
		int v=e[i].to;
		if(v==fa) continue;
		dfs(v,u);
	}
	return;
}
int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1;i<=n;i++) fa[i]=i;
	for(int i=1;i<=n;i++) scanf("%d",&d[i]);
	for(int i=1;i<=n;i++) root[i]=-1;
	int u,v;
	for(int i=1;i<=m;i++)
	{
		scanf("%d%d",&u,&v);
		if(find(u)==find(v)) continue;
		if(d[u]>d[v]) swap(u,v);
		if(d[u]==d[v]&&use[u]&&use[v]) continue;
		if(use[v]&&d[u]!=d[v]) continue;
		if(d[u]==d[v]) use[u]=use[v]=1;
		else use[v]=1;
		w[i]=max(d[u],d[v]);
		mer(u,v);
		add(u,v);
		add(v,u);
	}
	for(int i=1;i<=n;i++) 
	{
		if(!use[i])
		{
			printf("-1\n");
			return 0;			
		}
	}
	for(int i=1;i<=n;i++)
	{
		if(root[find(i)]==-1||d[root[find(i)]]>d[i]) root[find(i)]=i;
	}
	for(int i=1;i<=n;i++)
	{
		if(fa[i]==i)
		{
			dfs(root[i],0);
		}
	}
	for(int i=1;i<=n;i++) 
	{
		if(col[i]) printf("W");
		else printf("B");
	}
	printf("\n");
	for(int i=1;i<=m;i++)
	{
		if(w[i]==0) printf("1000000000\n");
		else printf("%d\n",w[i]);
	}
	return 0;
}