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() {
	long long N, M;
	vector<long long> D;
	vector<pair<long long, long long> > V;
	vector<long long> ANS;
	vector<bool> check;
	vector<long long> C;
	cin >> N >> M;
	D.resize(N), V.resize(M), C.assign(N, 2), ANS.resize(M), check.assign(N, false);
	for (int i = 0; i < N; i++) cin >> D[i];
	for (int i = 0; i < M; i++) {
		cin >> V[i].first >> V[i].second;
		V[i].first--, V[i].second--;
		if (D[V[i].first] == D[V[i].second]) {
			check[V[i].first] = check[V[i].second] = true;
			ANS[i] = D[V[i].first];
			if (C[V[i].first] == 2) {
				if (C[V[i].second] == 2) C[V[i].first] = 0, C[V[i].second] = 1;
				else C[V[i].first] = 1 - C[V[i].second];
			}
			else {
				if (C[V[i].second] == 2) C[V[i].second] = 1 - C[V[i].first];
			}
		}
		else {
			if (D[V[i].first] > D[V[i].second]) check[V[i].first] = true;
			else check[V[i].second] = true;
		}
	}
	for (int i = 0; i < N; i++) {
		if (!check[i]) {
			cout << -1 << endl;
			return 0;
		}
	}
	for (int i = 0; i < N; i++) {
		if (C[i] == 2) cout << 'W', C[i] = 0;
		else cout << (C[i] == 0 ? 'W' : 'B');
	}
	cout << endl;
	for (int i = 0; i < M; i++) {
		long long S = V[i].first, T = V[i].second;
		if (C[S] == C[T]) {
			if (D[S] == D[T]) ANS[i] = D[S];
			else ANS[i] = abs(D[S] - D[T]);
		}
		else ANS[i] = max(D[S], D[T]);
	}
	for (int i = 0; i < M; i++) cout << ANS[i] << endl;
}