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;
#define int long long
const int MOD = 1000000007;

signed main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	int N, M;
	cin >> N >> M;
	vector<pair<int, int> > A(N);
	vector<int> D(N);
	for (int i = 0; i < N; i++) {
		cin >> A[i].first;
		D[i] = A[i].first;
		A[i].second = i;
	}
	vector<vector<pair<int, int> > > g(N);
	int INF = 1000000000;
	vector<int> res(M, INF);
	for (int i = 0; i < M; i++) {
		int a, b;
		cin >> a >> b;
		a--;
		b--;
		g[a].emplace_back(b, i);
		g[b].emplace_back(a, i);
	}
	sort(A.begin(), A.end());
	string col(N, '.');
	for (int i = 0; i < N; i++) {
		int val = A[i].first;
		int idx = A[i].second;
		if (col[idx] != '.') continue;
		bool ok = false;
		for (const pair<int, int> &p : g[idx]) {
			if (col[p.first] != '.') {
				col[idx] = (col[p.first] == 'B' ? 'W' : 'B');
				res[p.second] = val;
				ok = true;
				break;
			}
		}
		if (!ok) {
			queue<int> qu;
			qu.push(idx);
			col[idx] = 'B';
			while (qu.size() > 0) {
				int a = qu.front();
				qu.pop();
				for (const pair<int, int> &p : g[a]) {
					if (col[p.first] == '.') {
						if (D[p.first] == val) {
							col[p.first] = (col[a] == 'B' ? 'W' : 'B');
							res[p.second] = val;
							ok = true;
							qu.push(p.first);
						}
					}
				}
			}
		}
		if (!ok) {
			cout << -1 << endl;
			return 0;
		}
	}
	cout << col << endl;
	for (int i = 0; i < M; i++) {
		cout << res[i] << endl;
	}
}