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=1e5+5,inf=1e9;
struct Edge{
	int next,to;
}edge[N<<2];
struct Node{
	int w,x;
	bool operator < (const Node &b)const{return w<b.w;}
}a[N];
int fi[N],se=1,c[N],d[N],ans[N<<1];
inline void add_edge(int u,int v){edge[++se].next=fi[u],edge[se].to=v,fi[u]=se;}
inline void add(int u,int v){add_edge(u,v),add_edge(v,u);}
void dfs(int x){
	for(int i=fi[x];i;i=edge[i].next){
		int v=edge[i].to;
		if(c[v]){c[x]=c[v]^3,ans[i>>1]=d[x];return;}
		if(d[v]==d[x]){c[x]=1,c[v]=2,ans[i>>1]=d[x];return;}
	}
	puts("-1");exit(0);
}
int main(){
	int n,m,u,v;scanf("%d%d",&n,&m);
	for(int i=0;i<n;i++)scanf("%d",d+i+1),a[i].w=d[i+1],a[i].x=i+1;
	for(int i=0;i<m;i++)scanf("%d%d",&u,&v),add(u,v);
	sort(a,a+n);
	for(int i=0;i<n;i++)if(!c[a[i].x])dfs(a[i].x);
	for(int i=1;i<=n;i++)if(c[i]==1)putchar('B');else putchar('W');
	for(int i=1;i<=m;i++)printf("\n%d",ans[i]?ans[i]:inf);
	return 0;
}