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 <cstdio>
#include <vector>
#include <queue>
#include <utility>
#include <algorithm>
using namespace std;
vector<int> e[100010];
int u[200010], v[200010], w[200010], d[100010];
char c[100010];
int fi[100010], nw;
pair<int, int> p[100010];
int dfs(int x) {
	int res = 0;
	for (int i = 0; i < e[x].size(); i++) {
		int z = e[x][i], y = u[z] + v[z] - x;
		if (!fi[y] || c[y]) continue;
		c[y] = 3 - c[x];
		w[z] = nw;
		dfs(y);
		res = 1;
	}
	return res;
}
int main() {
	int n, m;
	scanf("%d%d", &n, &m);
	for (int i = 0; i < n; i++) {
		scanf("%d", &d[i]);
	}
	for (int i = 0; i < m; i++) {
		scanf("%d%d", &u[i], &v[i]);
		--u[i]; --v[i];
		e[u[i]].push_back(i);
		e[v[i]].push_back(i);
	}
	for (int i = 0; i < n; i++) {
		p[i] = make_pair(d[i], i);
	}
	sort(p, p + n);
	int st = 0;
	while (st < n) {
		int ed = st;
		while (ed < n && p[st].first == p[ed].first) {
			fi[p[ed].second] = 1;
			ed++;
		}
		nw = p[st].first;
		for (int i = st; i < ed; i++) {
			int x = p[i].second;
			if (c[x]) continue;
			for (int j = 0; j < e[x].size(); j++) {
				int z = e[x][j], y = u[z] + v[z] - x;
				if (c[y]) {
					c[x] = 3 - c[y];
					w[z] = nw;
					dfs(x);
					break;
				}
			}
		}
		for (int i = st; i < ed; i++) {
			int x = p[i].second;
			if (c[x]) continue;
			c[x] = 1;
			if (!dfs(x)) {
				puts("-1");
				return 0;
			}
		}
		st = ed;
	}
	for (int i = 0; i < n; i++) {
		c[i] = c[i] == 1 ? 'B' : 'W';
	}
	puts(c);
	for (int i = 0; i < m; i++) {
		if (!w[i]) w[i] = 1000000000;
		printf("%d\n", w[i]);
	}
	return 0;
}