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(int i=0; i<(n); i++)
using P = pair<int,int>;
int n, m, v, u, d[100005], ans[200005];
char ans2[100005];
vector<P> G[100005], G2[100005];
void dfs(int u, int p, int c){
	ans2[u] = c ? 'B' : 'W';
	for(P nx: G2[u]) if(nx.first != p) dfs(nx.first, u, c ^ nx.second);
}
int main(){
	scanf("%d%d", &n, &m);
	fill(ans, ans+m, (int)1e9);
	rep(i,n) scanf("%d", d+i);
	rep(i,m){
		scanf("%d%d", &v, &u);
		v--; u--;
		G[v].push_back(P{u,i});
		G[u].push_back(P{v,i});
	}
	rep(i,n){
		bool ok = false;
		for(P p: G[i]) if(d[p.first] <= d[i]){
			int tmp = d[p.first] == d[i];
			ans[p.second] = d[i] - (1-tmp) * d[p.first];
			G2[p.first].push_back({i,tmp});
			G2[i].push_back({p.first,tmp});
			ok = true;
			break;
		}
		if(!ok) return puts("-1") * 0;
	}
	rep(i,n) if(ans2[i] == '\0') dfs(i,i,0);
	printf("%s\n", ans2);
	rep(i,m) printf("%d\n", ans[i]);
}