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 <vector>
#include <utility>
#include <queue>
using namespace std;
int INF = 1000000000;
int main(){
	int N, M;
	cin >> N >> M;
	vector<int> D(N);
	for (int i = 0; i < N; i++){
		cin >> D[i];
	}
	vector<vector<pair<int, int>>> E(N);
	for (int i = 0; i < M; i++){
		int U, V;
		cin >> U >> V;
		U--;
		V--;
		E[U].push_back(make_pair(i, V));
		E[V].push_back(make_pair(i, U));
	}
	vector<int> C(N, -1);
	vector<int> W(M, INF);
	queue<int> Q;
	for (int v = 0; v < N; v++){
		for (auto P : E[v]){
			int id = P.first;
			int w = P.second;
			if (D[v] == D[w]){
				if (C[v] == -1){
					if (C[w] == -1){
						C[v] = 0;
						C[w] = 1;
						W[id] = D[v];
						Q.push(v);
						Q.push(w);
					} else {
						C[v] = 1 - C[w];
						W[id] = D[v];
						Q.push(v);
					}
				} else if (C[w] == -1){
					C[w] = 1 - C[v];
					W[id] = D[v];
					Q.push(w);
				}
			}
		}
	}
	while (!Q.empty()){
		int v = Q.front();
		Q.pop();
		for (auto P : E[v]){
			int id = P.first;
			int w = P.second;
			if (C[w] == -1 && D[w] > D[v]){
				C[w] = 1 - C[v];
				W[id] = D[w];
				Q.push(w);
			}
		}
	}
	bool ok = true;
	for (int i = 0; i < N; i++){
		if (C[i] == -1){
			ok = false;
		}
	}
	if (!ok){
		cout << -1 << endl;
	} else {
		for (int i = 0; i < N; i++){
			if (C[i] == 0){
				cout << 'W';
			}
			if (C[i] == 1){
				cout << 'B';
			}
		}
		cout << endl;
		for (int i = 0; i < M; i++){
			cout << W[i] << endl;
		}
	}
}