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<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<set>
#include<unordered_set>
#include<unordered_map>
using namespace std;
typedef long long ll;
#define chmax(a,b) a=max(a,b)
#define chmin(a,b) a=min(a,b)
#define all(x) x.begin(),x.end()
#define rep(i,n) for(int i=0;i<n;i++)
#define mod 1000000007
#define mad(a,b) a=(a+b)%mod
#define N 200010
vector<ll> g[N];
ll n,m,a[N],b[N],c[N],d[N],len[N];
vector<ll> f[N];
bool us[N];
ll col[N];
void dfs(ll x,bool co){
    if(~col[x])return;
    col[x]=co;
    for(auto y:f[x]){
	dfs(y,co^1);
    }
}
int main(){
    cin>>n>>m;
    rep(i,n)cin>>d[i];
    rep(i,m){
	cin>>a[i]>>b[i];
	a[i]--,b[i]--;
	len[i]=max(d[a[i]],d[b[i]]);
	g[a[i]].push_back(i);
	g[b[i]].push_back(i);
    }
    bool ok=1;
    rep(i,n){
	ll mi=1e17,eid=0;
	for(auto e:g[i]){
	    if(mi>len[e]){
		eid=e;
		mi=len[e];
	    }
	}
	us[eid]=1;
	if(d[i]!=mi)ok=0;
    }
    if(ok==0){
	cout<<-1<<endl;
	return 0;
    }
    rep(i,m)if(us[i]){
	f[a[i]].push_back(b[i]);
	f[b[i]].push_back(a[i]);
    }
    rep(i,n)col[i]=-1;
    rep(i,n)dfs(i,0);
    rep(i,n)cout<<(col[i]?"B":"W"); cout<<endl;
    rep(i,m)cout<<len[i]<<endl;
}