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;
#define ll long long
const int N=1e5+5,M=N*2;
int n,m,d[N],p[N],e[N],f[N],id[N],w[M];
inline bool cmp(int x,int y){return d[x]<d[y];}
int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1;i<=n;i++)scanf("%d",&d[i]),p[i]=i;
	sort(p+1,p+n+1,cmp);
	for(int i=1,u,v;i<=m;i++)
	{
		scanf("%d%d",&u,&v);
		if(d[u]==d[v])
		{
			if(!f[u]&&!f[v])f[u]=1;
			if(!f[u])f[u]=-f[v];
			if(!f[v])f[v]=-f[u];
			if(f[u]==-f[v])w[i]=d[u];
		}
		else
		{
			if(d[u]<d[v])swap(u,v);
			e[u]=v;id[u]=i;
		}
	}
	for(int i=1,x;i<=n;i++)if(!f[x=p[i]])
	{
		if(!e[x]){puts("-1");return 0;}
		f[x]=f[e[x]];w[id[x]]=d[x]-d[e[x]];
	}
	for(int i=1;i<=n;i++)putchar(f[i]>0?'B':'W');
	for(int i=1;i<=m;i++)printf("\n%d",w[i]?w[i]:1000000000);
	return 0;
}