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(){
	int N, M, i, j, k;
	scanf("%d%d", &N, &M);
	vector<int> D(N);
	vector<pair<int, int>> D_id(N);
	for(i = 0; i < N; i++){
		scanf("%d", &D[i]);
		D_id[i].first = D[i];
		D_id[i].second = i;
	}
	vector<vector<int>> g(N, vector<int>(0)), edge_id(N, vector<int>(0));
	for(i = 0; i < M; i++){
		int U, V;
		scanf("%d%d", &U, &V);
		U--;
		V--;
		g[U].push_back(V);
		edge_id[U].push_back(i);
		g[V].push_back(U);
		edge_id[V].push_back(i);
	}
	sort(D_id.begin(), D_id.end());
	vector<int> color(N, -1), C(M, -1);
	for(k = 0; k < N; k++){
		int d = D_id[k].first;
		i = D_id[k].second;
		int equal_less_than_count = 0;
		int O_near = 0;
		for(j = 0; j < g[i].size(); j++){
			if(D[g[i][j]] <= D[i]){
				equal_less_than_count++;
				C[edge_id[i][j]] = d;
			}
			if(color[g[i][j]] == 0){
				O_near = 1;
			}
		}
		if(equal_less_than_count == 0){
			printf("-1\n");
			return 0;
		}
		color[i] = O_near;
	}
	for(i = 0; i < N; i++){
		if(color[i] == 0){
			printf("W");
		}
		else{
			printf("B");
		}
	}
	printf("\n");
	for(i = 0; i < M; i++){
		printf("%d\n", C[i]);
	}
	return 0;
}