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>
#define N 100100
#define M 200100
using namespace std;
int d[N];
int id[N];
int c[N];
int ex[M],ey[M],ans[M];
char col[N];
vector<int> g[N];
bool cmp(int i,int j){
	return d[i]<d[j];
}
int main(){
	int n,m;
	bool fail=false;
	scanf("%d%d",&n,&m);
	for(int i=1;i<=n;i++) scanf("%d",&d[i]);
	for(int i=0;i<m;i++){
		scanf("%d%d",&ex[i],&ey[i]);
		g[ex[i]].push_back(i);
		g[ey[i]].push_back(i);
	}
	for(int i=0;i<n;i++) id[i]=i+1;
	sort(id,id+n,cmp);
	for(int i=0;i<n;i++){
		int u=id[i];
		fail=true;
		for(int j=0;j<g[u].size();j++){
			int t=g[u][j];
			int v=ex[t]^ey[t]^u;
			if(d[v]<=d[u]){
				fail=false;
				ans[t]=d[u];
				if(!col[u]){
					if(col[v]=='B') col[u]='W';
					else if(col[v]=='W') col[u]='B';
					else{
						col[u]='B';
						col[v]='W';
					}
				}					
			}
		}
		if(fail) break;
	}
	if(fail) puts("-1");
	else{
		puts(col+1);
		for(int i=0;i<m;i++) printf("%d\n",ans[i]);
	}
	return 0;
}