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>
#define LL long long
#define PII pair<int, int>
#define f first
#define s second 
using namespace std;
const LL INF = (LL) 1e9 + 5;
const LL MOD = (LL) 1e9 + 7;
const int MAXN = 300005;

struct DSU {
	int pa[MAXN], sz[MAXN];
	void init(int n) {
		for (int i = 0; i <= n; i++) {
			pa[i] = i;
			sz[i] = 1;
		}
	}
	int find(int x) {
		return x == pa[x] ? x : x = find(pa[x]);
	}
	int merge(int x, int y) {
		x = find(x); y = find(y);
		if (x == y) return 0;
		if (sz[x] < sz[y]) swap(x, y);
		sz[x] += sz[y];
		pa[y] = x;
		return 1;
	}
} ds;

struct Edge {
	int to, id;
};

int n, m, d[MAXN], w[MAXN], col[MAXN], dep[MAXN];
Edge pa[MAXN];
vector<Edge> G[MAXN];
vector<int> ch[MAXN];

void dfs(int v, int d) {
	dep[v] = d;
//	cout << "DFS " << v << " " << d << '\n';
	for (int to : ch[v]) {
		dfs(to, d + 1);
	}
}

int main() {
	ios_base::sync_with_stdio(0); cin.tie(0);

	cin >> n >> m;
	for (int i = 1; i <= n; i++) {
		cin >> d[i];
	}
	for (int i = 1; i <= m; i++) {
		int u, v;
		cin >> u >> v;
		G[u].push_back({v, i});
		G[v].push_back({u, i});
		w[i] = (int) 1e9;
	}
	
	ds.init(n);
	for (int i = 1; i <= n; i++) {
		int ok = 0;
		for (Edge e : G[i]) {
			if (d[e.to] <= d[i]) {
				ok = 1;
				if (ds.merge(i, e.to)) {
					pa[i] = e;
					ch[e.to].push_back(i);
					w[e.id] = d[i];
				}
				break;
			}
		}
		if (!ok) {
			cout << "-1\n";
			return 0;
		}
	}
	
	for (int i = 1; i <= n; i++) {
//		cout << "At " << i << " " << pa[i].to << '\n';
		if (pa[i].to == 0) {
			dfs(i, 1);
		}
	}
	
	for (int i = 1; i <= n; i++) {
		assert(dep[i] != 0);
		cout << (dep[i] % 2 ? "B" : "W");
	}
	cout << '\n';
	for (int i = 1; i <= m; i++) {
		cout << w[i] << '\n';
	}

	return 0;
}