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:
#define _USE_MATH_DEFINES

#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <vector>
#include <queue>
#include <map>
#include <set>
#include <unordered_map> 
#include <unordered_set>
#include <functional>

using namespace std;

typedef pair<long long int, long long int> P;
typedef tuple<int, int, int> T;

long long int INF = 1e18;
long long int MOD = 1e9 + 7;

long long int D[110000];
int memo[110000];
vector<P> E[110000];
long long int ans[210000];
bool used[110000];

int main(){
	int N, M;
	cin >> N >> M;
	vector<P> v;
	for(int i = 1; i <= N; i++){
		cin >> D[i];
		v.push_back(P(D[i], i));
	}
	for(int i = 0; i < M; i++){
		int u, v;
		cin >> u >> v;
		E[u].push_back(P(v, i));
		E[v].push_back(P(u, i));
	}
	sort(v.begin(), v.end());
	for(P p : v){
		int pos = p.second;
		if(used[pos]){
			continue;
		}
		int les;
		P e;
		bool flag = true;
		for(P ed : E[pos]){
			int to = ed.first;
			if(D[to] <= D[pos]){
				flag = false;
				les = to;
				e = ed;
			}
		}
		if(flag){
			cout << -1 << endl;
			return 0;
		}
		if(memo[les] == 0){
			memo[pos] = 1;
			memo[les] = -1;
			used[les] = true;
		}else if(memo[les] == 1){
			memo[pos] = -1;
		}else{
			memo[pos] = 1;
		}
		ans[e.second] = D[pos];
	}
	for(int i = 1; i <= N; i++){
		if(memo[i] == 1){
			cout << "B";
		}else{
			cout << "W";
		}
	}
	cout << endl;
	for(int i = 0; i < M; i++){
		if(ans[i] == 0){
			cout << (int)1e9 << endl;
		}else{
			cout << ans[i] << endl;
		}
	}
	return 0;
}