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<cstdio>
#include<algorithm>
const int N=100007;
int read(){int x;scanf("%d",&x);return x;}
int d[N],p[N],e[N],f[N],id[N],w[N*2];
int main()
{
    int n=read(),m=read();
    for(int i=1;i<=n;++i) d[p[i]=i]=read();
    std::sort(p+1,p+n+1,[](int i,int j){return d[i]<d[j];});
    for(int i=1,u,v;i<=m;++i)
	if(d[u=read()]==d[v=read()])
	{
	    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]) std::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]) return puts("-1"),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);
}