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 <iostream>
#include <algorithm>
#include <utility>
#include <vector>
#define llint long long
#define inf 1e18

using namespace std;
typedef pair<llint, llint> P;

llint n, m;
llint d[100005];
vector<P> G[100005];
vector<P> vec;
llint color[100005];
llint w[200005];

int main(void)
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	
	cin >> n >> m;
	for(int i = 1; i <= n; i++){
		cin >> d[i];
		vec.push_back(P(d[i], i));
	}
	sort(vec.begin(), vec.end());
	
	llint u, v;
	for(int i = 1; i <= m; i++){
		cin >> u >> v;
		G[u].push_back(P(v, i));
		G[v].push_back(P(u, i));
	}
	
	for(int i = 0; i < vec.size(); i++){
		llint v = vec[i].second;
		if(color[v]) continue;
		bool flag = false;
		//cout << v << endl;
		for(int j = 0; j < G[v].size(); j++){
			llint u = G[v][j].first, e = G[v][j].second;
			if(d[u] > d[v]) continue;
			if(d[u] == d[v]){
				if(color[u] == 0) color[u] = -1, color[v] = 1;
				else color[v] = -color[u];
				//cout << v << " " << u << " " << color[u] << " " << color[v] << endl;
				w[e] = d[v];
				flag = true;
				break;
			}
			if(d[u] < d[v]){
				color[v] = color[u];
				w[e] = d[v] - d[u];
				flag = true;
				break;
			}
		}
		if(!flag){
			cout << -1 << endl;
			return 0;
		}
	}
	
	for(int i = 1; i <= n; i++){
		if(color[i] > 0) cout << "B";
		else cout << "W";
	}
	cout << endl;
	for(int i = 1; i <= m; i++){
		if(w[i] == 0) w[i] = 1000000000;
		cout << w[i] << endl;
	}
	
	return 0;
}