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;

#define REP(i,n) for(ll (i) = (0);(i) < (n);++i)
#define REV(i,n) for(ll (i) = (n) - 1;(i) >= 0;--i)
#define PB push_back
#define EB emplace_back
#define MP make_pair
#define FI first
#define SE second
#define SHOW1d(v,n) {REP(WW,n)cerr << v[WW] << ' ';cerr << endl << endl;}
#define SHOW2d(v,WW,HH) {REP(W_,WW){REP(H_,HH)cerr << v[W_][H_] << ' ';cerr << endl;}cerr << endl;}
#define ALL(v) v.begin(),v.end()
#define Decimal fixed<<setprecision(20)
#define INF 1000000000
#define LLINF 1000000000000000000LL
#define MOD 998244353

typedef long long ll;
typedef pair<ll,ll> P;

vector<vector<P>> v(111111);
ll d[111111];
ll c[222222];
ll color[111111];
ll used[111111];

int main(){
	cin.tie(0);cout.tie(0);ios::sync_with_stdio(false);

	ll n, m;cin >> n >> m;
	REP(i, n)cin >> d[i];
	REP(i, m){
		ll a, b;cin >> a >> b;
		a--;b--;
		v[a].EB(b, i);
		v[b].EB(a, i);
	}

	queue<ll> q;
	REP(i, n){
		REP(j, v[i].size()){
			int aite = v[i][j].FI;
			int edge_id = v[i][j].SE;
			if(d[i] == d[aite]){
				if(color[i] != 0 && color[aite] != 0)continue;
				if(color[i] == 0){
					if(color[aite] != 0)color[i] = -color[aite];
					else color[i] = 1;
				}
				if(color[aite] == 0)color[aite] = -color[i];
				q.push(i);
				q.push(aite);
				c[edge_id] = d[i];
			}
		}
	}

	while(!q.empty()){
		int id = q.front();q.pop();
		//cout << "id " << id << endl;
		if(used[id])continue;
		used[id] = true;
		REP(i, v[id].size()){
			int aite = v[id][i].FI;
			int edge_id = v[id][i].SE;
			//cout << " " << aite << endl;
			if(used[aite])continue;
			if(d[aite] <= d[id])continue;
			if(color[aite] != 0)continue;
			color[aite] = color[id];
			c[edge_id] = d[aite] - d[id];
			q.push(aite);
		}
	}

	REP(i, n){
		if(!used[i]){
			cout << -1 << endl;
			return 0;
		}
	}

	REP(i, n)cout << (color[i] == 1 ? 'B' : 'W');cout << endl;
	REP(i, m)cout << (c[i] == 0 ? INF : c[i]) << endl;

	return 0;
}