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 fo(i,a,b) for((i)=(a);i<=(b);i++)
#define rfo(i,a,b) for((i)=(a);i>=(b);i--)
#define inrange(x,y,z) (((x)>=(y))&&((x)<=(z)))
#define ALL(vec) ((vec).begin(),(vec).end())
#define SOR(vec) sort(ALL(vec))
#define UNI(vec) (vec).erase(unique(ALL(vec)),(vec).end())
using namespace std;
int n,m,uu,vv,d[100100],c[200100],co[100100];
vector<int> ga[100100];
vector<pair<int,int> > cand[100100];
pair<int,int> nxt[100100];
void search(int u){
	int v=nxt[u].first;
	if(!co[v]) search(v);
	co[u]=3-co[v];
	c[nxt[u].second]=d[u];
}
int main(){
	#ifdef FILIN
		#ifndef DavidDesktop
			freopen(FILIN,"r",stdin);
			freopen(FILOUT,"w",stdout);
		#endif
	#endif
	ios::sync_with_stdio(0);
	cin.tie(NULL);
	cout.tie(NULL);
	cin>>n>>m;
	for(int i=1;i<=n;i++) cin>>d[i];
	for(int i=1;i<=m;i++){
		cin>>uu>>vv;
		ga[uu].push_back(vv);
		ga[vv].push_back(uu);
		if(d[uu]>=d[vv]) cand[uu].push_back(make_pair(vv,i));
		if(d[vv]>=d[uu]) cand[vv].push_back(make_pair(uu,i));
	} 
	for(int i=1;i<=n;i++){
		if(cand[i].size()==0){cout<<-1<<endl;return 0;}
		nxt[i]=cand[i][0];
	}
	for(int i=1;i<=n;i++){
		int j=nxt[i].first;
		if(nxt[j].first==i){
			c[nxt[i].second]=d[i];
			co[i]=1;
			co[j]=2;
		}
	}
	for(int i=1;i<=n;i++){
		if(!co[i]){
			search(i);
		}
	}
	for(int i=1;i<=n;i++){
		if(co[i]==1) cout<<"W";
		else cout<<"B";
	}
	cout<<endl;
	for(int i=1;i<=m;i++){
		if(!c[i]) c[i]=1e9;
		cout<<c[i]<<endl;
	}
	cout<<endl;
	return 0;
}