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;

int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	
	int n,m;
	cin >> n >> m;
	vector<long long> d(n);
	for(int i=0;i<n;i++) cin >> d[i];
	
	vector<pair<int,int>> ed(m);
	vector<vector<int>> ad(n);
	for(int i=0;i<m;i++){
		int a,b;
		cin >> a >> b;
		a--,b--;
		ed[i]={a,b};
		ad[a].push_back(b);
		ad[b].push_back(a);
	}
	
	vector<int> ind(n);
	for(int i=0;i<n;i++) ind[i]=i;
	sort(ind.begin(),ind.end(),
		[&](int i0,int i1){
			return d[i0]<d[i1];
		}
	);
	
	for(int i=0;i<n;i++){
		bool bo2=false;
		for(int ch:ad[i]){
			if(d[ch]<=d[i]){
				bo2=true;
			}
		}
		if(!bo2){
			cout << -1 << "\n";
			return 0;
		}
	}
	
	map<pair<int,int>,long long> mp;
	set<pair<int,int>> st;
	
	vector<vector<int>> ad2(n);
	for(int i=0;i<n;i++){
		int cur=ind[i];
		
		int par=-1;
		for(int ch:ad[cur]){
			if(par==-1) par=ch;
			else{
				if(d[par]>d[ch]) par=ch;
			}
		}
		ad2[cur].push_back(par);
		ad2[par].push_back(cur);
		
		for(int ch:ad[cur]){
			if(ch==par) continue;
			if(st.find({ch,cur})!=st.end()) continue;
			mp[{cur,ch}]=1000000000;
			mp[{ch,cur}]=1000000000;
		}
		mp[{cur,par}]=d[cur];
		mp[{par,cur}]=d[cur];
		st.insert({par,cur});
		st.insert({cur,par});
	}
	
	vector<int> c(n);
	function<void(int,int)> dfs=[&](int cur,int par){
		for(int ch:ad2[cur]){
			if(ch==par) continue;
			if(c[ch]==0){
				c[ch]=3-c[cur];
				dfs(ch,cur);
			}
		}
	};
	for(int i=0;i<n;i++){
		if(c[i]==0){
			c[i]=1;
			dfs(i,-1);
		}
	}
	for(int i=0;i<n;i++){
		if(c[i]==1) cout << "W";
		else cout << "B";
	}
	cout << "\n";
	for(int i=0;i<m;i++){
		cout << mp[ed[i]] << "\n";
	}
	return 0;
}