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=2e5+5;
int n,m,d[N],u[N],v[N],w[N],i,e[N];
char c[N];
void E(){puts("-1");exit(0);}
int main(){
	scanf("%d%d",&n,&m);
	for(i=1;i<=n;++i)scanf("%d",d+i);memset(c+1,-1,n);
	for(i=1;i<=m;++i)scanf("%d%d",u+i,v+i),e[i]=i,w[i]=max(d[u[i]],d[v[i]]);
	sort(e+1,e+m+1,[&](int x,int y){return w[x]<w[y];});
	for(i=1;i<=m;++i){
		int x=u[e[i]],y=v[e[i]];
		if(c[x]==-1 && c[y]==-1){
			if(d[x]!=d[y])E();
			c[x]=0;c[y]=1;
		}else if(c[x]==-1 || c[y]==-1){
			if(c[x]==-1){
				if(d[x]<d[y])E();
				c[x]=c[y]^1;
			}else{
				if(d[y]<d[x])E();
				c[y]=c[x]^1;
			}
		}else w[e[i]]=1e9;
	}
	for(i=1;i<=n;++i)if(c[i]==-1)E();
	for(i=1;i<=n;++i)putchar(c[i]==0?'W':'B');puts("");
	for(i=1;i<=m;++i)printf("%d\n",w[i]);
}