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;
typedef long long ll;

template<typename T>
ostream& operator<<(ostream &os, vector<T> &v){
	string sep = " ";
	if(v.size()) os << v[0];
	for(int i=1; i<v.size(); i++) os << sep << v[i];
	return os;
}

#ifdef DBG
void debug_(){ cout << endl; }
template<typename T, typename... Args>
void debug_(T&& x, Args&&... xs){
	cout << x << " "; debug_(forward<Args>(xs)...);
}
#define dbg(...) debug_(__VA_ARGS__);
#else
#define dbg(...) 
#endif

int main() {
	ios_base::sync_with_stdio(false);

	int n, m;
	cin >> n >> m;
	vector<int> d(n);
	vector<pair<int, int>> e(m);
	vector<vector<pair<int, int>>> graph(n);
	for(int i=0; i<n; i++) cin >> d[i];
	for(int i=0; i<m; i++){
		cin >> e[i].first >> e[i].second;
		e[i].first--;
		e[i].second--;
		graph[e[i].first].push_back({e[i].second, i});
		graph[e[i].second].push_back({e[i].first, i});
	}

	vector<pair<int, int>> ds(n);
	for(int i=0; i<n; i++) ds[i] = {d[i], i};

	sort(ds.begin(), ds.end());

	vector<pair<int, int>> es;
	for(int i=0; i<m; i++){
		if(d[e[i].first]!=d[e[i].second]) continue;
		es.push_back({d[e[i].first], i});
	}
	sort(es.begin(), es.end());

	vector<int> c(n);
	vector<int> x(m, 1e9);

	for(int i=0; i<n; i++){
		int v=ds[i].second;
		if(c[v]>0) continue;
		bool done = false;
		for(auto p: graph[v]){
			int u = p.first;
			if(c[u]>0){
				c[v] = 3-c[u];
				x[p.second] = ds[i].first;
				done=true;
				break;
			}
		}
		if(done) continue;

		for(auto p: graph[v]){
			int u = p.first;
			if(d[u]==d[v]){
				c[u] = 1;
				c[v] = 2;
				x[p.second] = ds[i].first;
				done = true;
				break;
			}
		}
		if(!done){
			cout << -1 << endl;
			return 0;
		}
	}

	string ans;
	for(int i=0; i<n; i++){
		if(c[i]==1) ans += "B";
		else ans += "W";
	}
	cout << ans << endl;
	for(int i=0; i<m; i++){
		cout << x[i] << endl;
	}

	return 0;
}