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;
#define fi first
#define se second
const int N=2e5+5;
struct node{
	int u,val;
	node () {}
	node (int _u,int _v){
		u = _u; val = _v;
	}
	bool operator < (const node &b) const {
		return val < b.val;
	}
};
priority_queue<node> q;
int a[N],n,m,col[N],val[N],vis[N];
vector< pair<int,int> > e[N];
int main(){
	cin>>n>>m;
	for(int i=1;i<=n;++i)
		cin>>a[i];
	int fl=1,u,v;
	for(int i=1;i<=m;++i){
		cin>>u>>v;
		e[u].push_back(make_pair(v,i));
		e[v].push_back(make_pair(u,i));
		if( a[u] == a[v] && !vis[u] && !vis[v])
			q.push(node(u,a[u])),
			q.push(node(v,a[v])),
			col[u]=1,col[v]=0,
			vis[u]=1,vis[v]=1,
			val[i]=a[u];
	}
	while(!q.empty()){
		int u=q.top().u,V=q.top().val;q.pop();
		for(int i=0;i<e[u].size();++i)
			if(!vis[e[u][i].fi] && a[e[u][i].fi]>=V)
				vis[e[u][i].fi]=1,q.push(node(e[u][i].fi,a[e[u][i].fi])),
				col[e[u][i].fi]=col[u]^1,val[e[u][i].se]=a[e[u][i].fi];
	}
	for(int i=1;i<=n;++i)
		if(!vis[i]) return puts("-1"),0;
	for(int i=1;i<=n;++i)
		cout<<(col[i]==0?"B":"W");
	cout<<endl;
	for(int i=1;i<=m;++i)
		cout<<(val[i]==0?(int)1e9:val[i])<<endl;
	return 0;
}