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 rep(i, n) for(int i=0; i<int(n); i++)
#define ALL(a) (a).begin(), (a).end()
using namespace std;
typedef long long ll;
typedef pair<int, int> P;

int N, M, INF = 1e9;
int used[100000], C[200000], S[100000];
vector<int> DD;
vector<P> G[100000];
vector<P> D;

int main(){
	cin >> N >> M;
	rep(i, N){ int d; cin >> d; D.push_back(P(d, i)); S[i] = -1; DD.push_back(d); }
	rep(i, M){
		int u, v; cin >> u >> v;
		u--; v--;
		G[u].push_back(P(v, i));
		G[v].push_back(P(u, i));
	}
	sort(ALL(D));
	rep(i, N){
		int now = D[i].second, f = 0;
		if(used[now]) continue;
		rep(j, G[now].size()){
			int to = G[now][j].first;
			if(DD[to] <= DD[now]){
				C[G[now][j].second] = DD[now];
				if(S[to] == -1) S[to] = 1;
				f = 1;
				S[now] = 1 - S[to];
				used[now] = 1;
				used[to] = 1;
				break;
			}
		}
		if(!f){ cout << -1 << endl; return 0; }
	}
	rep(i, N){
		if(S[i]) cout << 'W';
		else cout << 'B';
	}
	cout << "\n";
	rep(i, M){
		if(!C[i]) cout << INF << endl;
		else cout << C[i] << endl;
	}
	return 0;
}