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>
#pragma GCC target ("avx")
#pragma GCC optimization ("Ofast")
#pragma GCC optimization ("unroll-loops")
using namespace std;
#define int long long
#define rep(i,n) for(int i=0;i<n;i++)
#define REP(i,n) for(int i=1;i<n;i++)
#define rev(i,n) for(int i=n-1;i>=0;i--)
#define all(v) v.begin(),v.end()
#define P pair<int,int>
#define len(s) (int)s.size()

template<class T> inline bool chmin(T &a, T b){
	if(a>b){a=b;return true;}
	return false;
}
template<class T> inline bool chmax(T &a, T b){
	if(a<b){a=b;return true;}
	return false;
}
constexpr int mod = 1e9+7;
constexpr long long inf = 3e18;

int N,M,D[100005],A[200005],B[200005],C[200005];
vector<P>G[100005],G2[100005];
bool co[100005],used[100005];
void dfs(int x,int p){
	used[x]=true;
	for(auto i:G2[x])if(p!=i.first){
		C[i.second]=max(D[x],D[i.first]);
		co[i.first]=!co[x];
		dfs(i.first,x);
	}
}
signed main(){
	cin>>N>>M;
	rep(i,N)cin>>D[i];
	rep(i,M){
		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});
	}
	rep(i,N){
		int mn=inf,idx;
		rep(j,len(G[i]))if(chmin(mn,D[G[i][j].first]))idx=j;
		if(mn>D[i]){cout<<"-1\n";return 0;}
		G2[i].push_back(G[i][idx]);
		G2[G[i][idx].first].push_back({i,G[i][idx].second});
	}
	rep(i,N)if(!used[i])dfs(i,i);
	rep(i,N)cout<<(co[i]?"B":"W");
	cout<<"\n";
	rep(i,M)cout<<(C[i]?C[i]:(int)1e9)<<"\n";
}