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 rep(i,n) for(int i=0;i<(n);i++)

using namespace std;

template<class T> struct edge{
	int to;
	T wt;
	edge(int to,const T& wt):to(to),wt(wt){}
};
template<class T> using weighted_graph=vector<vector<edge<T>>>;

int main(){
	int n,m; scanf("%d%d",&n,&m);
	vector<int> val(n);
	rep(u,n) scanf("%d",&val[u]);
	weighted_graph<int> G(n);
	rep(i,m){
		int u,v; scanf("%d%d",&u,&v); u--; v--;
		G[u].emplace_back(v,i);
		G[v].emplace_back(u,i);
	}

	vector<pair<int,int>> p(n);
	rep(u,n) p[u]={val[u],u};
	sort(p.begin(),p.end());

	vector<int> color(n,-1),wt(m,1e9);
	rep(i,n){
		int u=p[i].second;
		if(color[u]!=-1) continue;

		int v=-1,id;
		for(auto e:G[u]) if(val[e.to]<=val[u]) { v=e.to; id=e.wt; break; }
		if(v==-1) return puts("-1"),0;

		if(color[v]==-1){
			color[u]=0;
			color[v]=1;
		}
		else{
			color[u]=1-color[v];
		}
		wt[id]=val[u];
	}

	rep(u,n) putchar(color[u]==0?'B':'W'); puts("");
	rep(i,m) printf("%d\n",wt[i]);

	return 0;
}