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 <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <cmath>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <algorithm>
#include <complex>
#include <unordered_map>
#include <unordered_set>
#include <random>
#include <cassert>
#include <fstream>
#include <utility>
#include <functional>
#include <time.h>
#include <stack>
#include <array>
#define popcount __builtin_popcount
using namespace std;
typedef long long int ll;
typedef pair<int, int> P;
int n, m;
bool used[100010];
int d[100010];
const int INF=1e9;
vector<P> g[100010];
int a[200020], b[200020];
int c[200020];
string s;
P p[100010];
int main()
{
	cin>>n>>m;
	for(int i=0; i<n; i++) cin>>d[i];
	for(int i=0; i<m; i++){
		cin>>a[i]>>b[i];
		a[i]--; b[i]--;
		g[a[i]].push_back({b[i], i});
		g[b[i]].push_back({a[i], i});
	}
	for(int i=0; i<n; i++) s+='B';
	for(int i=0; i<n; i++){
		p[i]=P(d[i], i);
	}
	sort(p, p+n);
	bool myon[100010]={};
	for(int i=0; i<n; i++){
		int x=p[i].second;
		int cnt=0, cnt1=0;
		for(auto q:g[x]){
			int y=q.first, k=q.second;
			if(d[y]>d[x]) continue;
			cnt1++;
		}
		if(cnt1==0){
			cout<<-1<<endl;
			return 0;
		}
		for(auto q:g[x]){
			int y=q.first, k=q.second;
			if(d[y]==d[x] && used[y] && myon[y]){
				c[k]=d[x];
				if(s[y]=='B') s[x]='W';
				else s[x]='B';
				cnt++;
			}
		}
		for(auto q:g[x]){
			int y=q.first, k=q.second;
			if(!used[y]) continue;
			if(cnt && !(d[y]==d[x] && myon[y])){
				c[k]=INF;
				continue;
			}
			if(d[y]<d[x]){
				c[k]=d[x]-d[y];
				s[x]=s[y];
				cnt++;
			}else{
				c[k]=d[x];
				if(s[y]=='B') s[x]='W';
				else s[x]='B';
				cnt++;
			}
		}
		used[x]=1;
		if(cnt==0) myon[x]=1;
	}
	cout<<s<<endl;
	for(int i=0; i<m; i++){
		cout<<c[i]<<endl;
	}
	return 0;
}