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 <stdio.h>
#include <algorithm>
#include <string>
#include <vector>
#include <numeric>
#include <queue>
#include <map>

const int mod = 1000000007;
//const int mod = 998244353;
int maximum(int a, int b) { return a < b ? b : a; }

int main() {
	long long N, M;
	scanf("%lld %lld", &N, &M);
	auto D = new int[N];
	for (int i = 0; i < N; i++) scanf("%d", D + i);
	auto U = new int[M];
	auto V = new int[M];
	std::map < long long, int>map;
	for (int i = 0; i < M; i++) {
		scanf("%d %d", U + i, V + i);
	}
	auto p = new std::vector<int>[N];
	for (int i = 0; i < M; i++) {
		U[i]--;
		V[i]--;
		p[U[i]].push_back(V[i]);
		p[V[i]].push_back(U[i]);
		map[U[i] * N + V[i]] = i;
		map[V[i] * N + U[i]] = i;
	}
	for (int i = 0; i < N; i++) {
		std::sort(p[i].begin(), p[i].end());
	}
	auto forest = new std::vector<int>[M];
	bool No = false;
	for (int i = 0; i < N; i++) {
		int min = 0;
		for (int j = 0; j < p[i].size(); j++) {
			if (D[p[i][j]] < D[p[i][min]]) {
				min = j;
			}
		}
		if (D[p[i][min]] > D[i]) {
			No = true;
			break;
		}
		forest[i].push_back(p[i][min]);
		forest[p[i][min]].push_back(i);
	}
	if (No) {
		printf("-1");
		return 0;
	}
	auto C = new char[N + 1]{};
	auto cost = new int[M] {};
	std::vector<int>q;
	int r = 0;
	for (int i = 0; i < N; i++) {
		if (C[i])continue;
		C[i] = 'B';
		q.push_back(i);
		while (q.size() > r) {
			for (int j = 0; j < forest[q[r]].size(); j++) {
				if (C[forest[q[r]][j]])continue;
				C[forest[q[r]][j]] = C[q[r]] == 'B' ? 'W' : 'B';
				cost[map[q[r] * N + forest[q[r]][j]]] = maximum(D[q[r]], D[forest[q[r]][j]]);
				q.push_back(forest[q[r]][j]);
			}
			r++;
		}
	}
	for (int i = 0; i < M; i++) {
		if (cost[i] == 0) {
			cost[i] = 1000000000;
		}
	}
	printf(C);
	for (int i = 0; i < M; i++) {
		printf("\n%d", cost[i]);
	}
	return 0;
}