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 MOD 1000000007LL
using namespace std;
typedef long long ll;
typedef pair<int,int> P;

int n,m;
int d[100005];
vector<P> G[100005];
int u[200005],v[200005];
int res[200005];
int col[100005];
int mini;
P p[100005];

bool check(){
	for(int i=0;i<n;i++){
		p[i]=P(d[i],i);
	}
	sort(p,p+n);
	for(int i=0;i<n;i++){
		int v=p[i].second;
		if(col[v]!=0){
			continue;
		}
		//printf("check%d\n",v);
		bool flag=false;
		for(int j=0;j<G[v].size();j++){
			int nv=G[v][j].first;
			if(d[v]==d[nv]){
				res[G[v][j].second]=d[v];
				if(col[nv]!=0){
					col[v]=-col[nv];
					flag=true;
					break;
				}else{
					col[v]=1;
					col[nv]=-1;
					flag=true;
					break;
				}
			}else if(d[v]>d[nv]){
				res[G[v][j].second]=d[v];
				col[v]=-col[nv];
				flag=true;
				break;
			}
		}
		if(!flag){
			return false;
		}
	}
	return true;
}

int main(void){
	scanf("%d%d",&n,&m);
	for(int i=0;i<n;i++){
		scanf("%d",&d[i]);
	}
	for(int i=0;i<m;i++){
		scanf("%d%d",&u[i],&v[i]);
		u[i]--;
		v[i]--;
		G[u[i]].push_back(P(v[i],i));
		G[v[i]].push_back(P(u[i],i));
	}
	mini=d[0];
	for(int i=0;i<n;i++){
		mini=min(mini,d[i]);
	}
	if(!check()){
		printf("-1\n");
		return 0;
	}

	for(int i=0;i<m;i++){
		if(res[i]==0){
			res[i]=1000000000;
		}
	}
	for(int i=0;i<n;i++){
		printf("%c",col[i]==1?'B':'W');
	}
	printf("\n");
	for(int i=0;i<m;i++){
		printf("%d\n",res[i]);
	}
	return 0;
}