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>

int ri() {
	int n;
	scanf("%d", &n);
	return n;
}

struct Hen {
	int x;
	int y;
	int id;
};

int main() {
	int n = ri();
	int m = ri();
	std::pair<int, int> all[n];
	for (int i = 0; i < n; i++) all[i].first = ri(), all[i].second = i;
	std::sort(all, all + n);
	
	std::vector<Hen> hen[n];
	for (int i = 0; i < m; i++) {
		int x = ri() - 1;
		int y = ri() - 1;
		hen[x].push_back({x, y, i});
		hen[y].push_back({y, x, i});
	}
	std::vector<int> cost(m, -1);
	std::vector<int> color(n, -1);
	bool ava[n];
	memset(ava, 0, sizeof(ava));
	int start = 0;
	for (int i = 0; i < n; i++) {
		if (i + 1 < n && all[i].first == all[i + 1].first) continue;
		// [start, i]
		std::set<int> newed;
		for (int j = start; j <= i; j++) ava[all[j].second] = true, newed.insert(all[j].second);
		for (int j = start; j <= i; j++) {
			int next = -1;
			int id = -1;
			for (auto k : hen[all[j].second]) {
				if (ava[k.y]) {
					next = k.y;
					id = k.id;
					break;
				}
			}
			// std::cerr << all[j].second << "->" << next << std::endl;
			if (color[all[j].second] != -1) continue;
			if (next == -1) {
				puts("-1");
				return 0;
			}
			if (cost[id] == -1) {
				cost[id] = all[i].first;
				if (color[next] == -1) color[next] = 0;
				color[all[j].second] = !color[next];
			} else assert(0);
		}
		
		start = i + 1;
	}
	for (auto &i : cost) if (i == -1) i = 1000000000;
	for (int i = 0; i < n; i++) {
		std::cout << (color[i] ? "B" : "W");
	}
	std::cout << std::endl;
	for (int i = 0; i < m; i++) std::cout << cost[i] << std::endl;
	
	return 0;
}