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;
typedef long long ll;
typedef pair<int, int> P;
const ll INFLL = (1ll<<60);
const int INF = (int)(1e9);

#define l_ength size

bool used[225816],visited[100100],color[100100];
int a[225816],b[225816],ans[225816],d[100100];

vector<P> g[100100];

void dfs(int u){
	int i,v,e;
	visited[u] = true;
	for(i=(g[u].l_ength()-1); i>=0; --i){
		v = g[u][i].first;
		e = g[u][i].second;
		if(!used[e]){
			continue;
		}
		if(visited[v]){
			continue;
		}
		color[v] = (!color[u]);
		dfs(v);
	}
}

int main(void){
	int n,m,u,v,i,j,e;
	bool flag;
	P tmp;
	fill(ans,ans+225816,INF);
	cin >> n >> m;
	for(i=0; i<n; ++i){
		cin >> d[i];
	}
	for(j=0; j<m; ++j){
		cin >> a[j] >> b[j];
		--a[j]; --b[j];
		g[a[j]].push_back(P(b[j],j));
		g[b[j]].push_back(P(a[j],j));
	}
	for(u=0; u<n; ++u){
		tmp = P(INF,INF);
		for(i=(g[u].l_ength()-1); i>=0; --i){
			v = g[u][i].first;
			e = g[u][i].second;
			tmp = min(tmp,P(d[v],v));
		}
		if(tmp.first > d[u]){
			cout << "-1" << endl;
			return 0;
		}
		for(i=(g[u].l_ength()-1); i>=0; --i){
			v = g[u][i].first;
			e = g[u][i].second;
			if(tmp.second == v){
				ans[e] = d[u];
				used[e] = true;
				break;
			}
		}
	}
	for(i=0; i<n; ++i){
		if(!visited[i]){
			dfs(i);
		}
		cout << ((color[i])?"B":"W");
	}
	cout << endl;
	for(j=0; j<m; ++j){
		cout << ans[j] << endl;
	}
	return 0;
}