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;

const int INF = 1000000000;

typedef pair<int,int> P;

#define fr first
#define sc second

int main(){
	static int n,m;
	static int d[100010];
	static int a[200010],b[200010];
	scanf("%d%d",&n,&m);
	for(int i = 1 ; i <= n ; i ++){
		scanf("%d",&d[i]);
	}
	for(int i = 1 ; i <= m ; i ++){
		scanf("%d%d",&a[i],&b[i]);
	}
	
	vector<int> G[100010];
	for(int i = 1 ; i <= m ; i ++){
		G[a[i]].push_back(b[i]);
		G[b[i]].push_back(a[i]);
	}
	
	vector<P> vec;
	for(int i = 1 ; i <= n ; i ++){
		vec.push_back(P(d[i],i));
	}
	sort(vec.begin(),vec.end());
	
	static int color[100010] = {};
	map<P,int> M;
	for(int i = 0 ; i < vec.size() ; i ++){
		int v = vec[i].sc;
		if(color[v] != 0)continue;
		int u = -1;
		for(int j = 0 ; j < G[v].size() ; j ++){
			if(d[G[v][j]] <= d[v]){
				u = G[v][j];
				break;
			}
		}
		if(u == -1){
			puts("-1");
			return 0;
		}
		if(color[u] == 0)color[u] = 1;
		color[v] = -color[u];
		M[P(u,v)] = d[v];
		M[P(v,u)] = d[v];
	}
	
	for(int i = 1 ; i <= n ; i ++){
		if(color[i] == 1)printf("B");
		else printf("W");
	}
	cout << endl;
	for(int i = 1 ; i <= m ; i ++){
		map<P,int>::iterator itr = M.find(P(a[i],b[i]));
		if(itr == M.end()){
			printf("%d\n",INF);
		}
		else printf("%d\n",itr->sc);
	}
}