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 F first
#define S second
#define pb push_back
#define all(x) x.begin(), x.end()

using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;

const int N = 200000 + 10;
const int MOD = 1000000007;
const int LOG = 20;
const int INF = 1000000010;
const int delta = 11353;

int n, D[N], m, mark[N], ans[N], ind[N];
vector<pii> G[N];

bool cmp(int x, int y){
	return D[x] < D[y];
}

int32_t main(){
	ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
	cin >> n >> m;
	memset(mark, -1, sizeof mark);
	for (int i = 1; i <= n; i++){
		ind[i] = i;
		cin >> D[i];
	}
	for (int i = 1; i <= m; i++){
		int v, u;
		cin >> v >> u;
		G[v].pb({u, i}), G[u].pb({v, i});
	}
	for (int i = 1; i <= n; i++){
		bool f = 0;
		for (auto u:G[i]){
			if (D[u.F] <= D[i]) f = 1;
		}
		if (!f) return cout << -1, 0;
	}
	sort(ind + 1, ind + n + 1, cmp);
	for (int i = 1; i <= n; i++){
		if (mark[ind[i]] != -1) continue;
		for (auto u:G[ind[i]]){
			if (D[u.F] <= D[ind[i]]){
				if (mark[u.F] == -1){
					mark[u.F] = 0;
					mark[ind[i]] = 1;
					ans[u.S] = D[ind[i]];
				}else{
					mark[ind[i]] = 1 - mark[u.F];
					ans[u.S] = D[ind[i]];
				}
			//	cout << "Fuck " << u.S << '\n';
				break;
			}
		}
	}
	for (int i = 1; i <= n; i++)cout << (mark[i]?'W':'B');
	cout << '\n';
	for (int i = 1; i <= m; i++){
		cout << (ans[i] == 0?1000000000:ans[i]) << '\n';
		//cout << ans[i] << '\n';
	}
	return 0;
}