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;
vector<pair<int,int> > G[N];
int d[N],id[N],col[N],val[N<<1];
bool cmp(int x,int y) {
	return d[x]<d[y];
}
int main() {
	int n,m;
	scanf("%d%d",&n,&m);
	for(int i=1;i<=n;i++) {
		scanf("%d",&d[i]);
		id[i]=i,col[i]=-1;
	}
	for(int i=1,u,v;i<=m;i++) {
		scanf("%d%d",&u,&v);
		G[u].push_back({v,i});
		G[v].push_back({u,i});
	}
	sort(id+1,id+n+1,cmp);
	for(int i=1;i<=n;i++) {
		int u=id[i];
		if(~col[u]) continue;
		bool f=false;
		for(auto it:G[u]) {
			int v=it.first;
			if(d[u]>=d[v]) {
				if(~col[v]) col[u]=col[v]^1;
				else col[v]=0,col[u]=col[v]^1;
				val[it.second]=d[u];
				f=true;
				break;
			}
		}
		if(!f) {
			printf("-1\n");
			return 0;
		}
	}
	for(int i=1;i<=n;i++) {
		printf("%c",col[i]?'W':'B');
	}
	printf("\n");
	for(int i=1;i<=m;i++) {
		if(!val[i]) val[i]=1e9;
		printf("%d\n",val[i]);
	}
	return 0;
}