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 syosu(x) fixed<<setprecision(x)
using namespace std;
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<string> vs;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<pll> vpll;
typedef pair<int,P> pip;
typedef vector<pip> vip;
const int inf=1<<30;
const ll INF=1ll<<60;
const double pi=acos(-1);
const double eps=1e-8;
const ll mod=1e9+7;
const int dx[4]={-1,0,1,0},dy[4]={0,-1,0,1};

int n,m;
vvp g;
vi a,b,c,vis,res;

void dfs(int v,int t){
	vis[v]=t;
	for(auto p:g[v]){
		int u=p.first,id=p.second;
		if(vis[u]!=t&&a[u]<=a[v]){
			res[id]=a[v];
			if(!vis[u]) dfs(u,t);
			b[v]=b[u]^1;
			break;
		}
	}
}

int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	cin>>n>>m;
	g=vvp(n);
	a=vis=b=vi(n);
	c=res=vi(m);
	for(auto &i:a) cin>>i;
	for(int i=0;i<m;i++){
		int u,v;
		cin>>u>>v;
		u--;v--;
		g[u].push_back({v,i});
		g[v].push_back({u,i});
	}
	bool B=0;
	for(int i=0;i<n;i++){
		bool flag=1;
		for(auto p:g[i]){
			int v=p.first;
			if(a[v]<=a[i]) flag=0;
		}
		B|=flag;
	}
	if(B){
		cout<<-1<<endl;
		return 0;
	}
	int id=1;
	for(int i=0;i<n;i++) if(!vis[i]) dfs(i,id++);
	for(int i=0;i<n;i++) cout<<(b[i]?'B':'W');
	cout<<endl;
	for(int i=0;i<m;i++){
		if(!res[i]) cout<<1000000000<<endl;
		else cout<<res[i]<<endl;
	}
}