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;
#define all(V) V.begin(),V.end()
#define ll long long
const ll MOD = 1000000007;

vector<pair<int,int>> G[200010];
char BW[200010];
map<pair<int,int>, int> edge;
int ans[200010];

int main() {
	int N, M, U, V, dis;
	cin >> N >> M;
	vector<int> D(N);
	vector<pair<int, int>> Ds(N);
	for (int i = 0;i < N;i++) {
		cin >> D[i];
		Ds[i] = { D[i],i };
	}
	sort(all(Ds));
	vector<pair<int, int>> Vs(M);

	for (int i = 0;i < M;i++) {
		cin >> U >> V;
		U--;V--;
		G[U].push_back(make_pair(D[V], V));
		G[V].push_back(make_pair(D[U], U));
		edge.insert({ {U,V},1000000000 });
		edge.insert({ {V,U},1000000000 });
		Vs[i] = { U,V };
	}

	for (int i = 0;i < N;i++) {
		sort(all(G[i]));
		BW[i] = 49;
	}

	
	int gs, fir, sec, s, t;
	for (int x = 0, i;x < N;x++) {
		i = Ds[x].second;
		dis = Ds[x].first;

		fir = G[i][0].first;
		sec = G[i][0].second;
		//for (int k = 0;k < N;k++)cout << BW[k];cout << endl;
		if (fir < dis) {
			if (BW[i] == 49) {
				edge[{i, sec}] = dis - fir;
				edge[{sec, i}] = dis - fir;
				BW[i] = BW[sec];
			}
		}
		else if (fir == dis) {
			edge[{i, sec}] = dis;
			edge[{sec, i}] = dis;
			if (BW[i] == 49) {
				if (BW[sec] == 'B')BW[i] = 'W';
				else BW[i] = 'B', BW[sec] = 'W';
			}
			else if (BW[sec] == 49) {
				if (BW[i] == 'B')BW[sec] = 'W';
				else BW[sec] = 'B';
			}
		}
		else {
			cout << -1 << endl;
			return 0;
		}
	}
	for (int i = 0;i < N;i++) {
		cout << BW[i];
	}
	cout << endl;

	for (int i = 0;i < M;i++) {
		cout << edge[Vs[i]] << endl;
	}
}