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>
#define ll long long
#define pb push_back
#define pii pair<int,int>
#define mp make_pair
#define fi first
#define se second
#define eb emplace_back
using namespace std;
const int mod = 1e9 + 7;
const int maxn = 2e5 + 233;
vector<int> g[maxn];
int d[maxn],vis[maxn];
int ord[maxn];
int ans[maxn],u[maxn],v[maxn];
queue<int> q;
map<pii,int> rev;
void shit(){
	puts("-1");
	exit(0);
}
bool cmp(int i,int j){
	return d[i]<d[j];
}
void cdd(int x,int y,int v){
	if(x>y)swap(x,y);
	int k = rev[mp(x,y)];
	ans[k] = v;
}
int main()
{
	int n,m;cin>>n>>m;
	for(int i=1;i<=n;i++)scanf("%d",&d[i]),ord[i] = i;
	sort(ord+1,ord+1+n,cmp);
//	if(d[ord[2]]!=d[ord[1]])shit();
	int mini = d[ord[1]];
	memset(vis,-1,sizeof(vis));
	for(int i=1;i<=m;i++){
		scanf("%d%d",&u[i],&v[i]);
		if(u[i]>v[i])swap(u[i],v[i]);
		rev[mp(u[i],v[i])] = i;
		g[u[i]].pb(v[i]);
		g[v[i]].pb(u[i]);
		ans[i] = 1e9;
	}
	for(int i=1;i<=n;i++){
		int x = ord[i];
		if(vis[x]!=-1)continue;
		for(int y:g[x]){
			if(vis[y]!=-1){
				vis[x] = vis[y]^1;
				cdd(x,y,d[x]);
				break;
			}
			if(d[y]==d[x]){
				vis[x] = 0;
				vis[y] = 1;
				cdd(x,y,d[x]);
				break;
			}
		}
	}
	for(int i=1;i<=n;i++)if(vis[i]==-1)shit();
	for(int i=1;i<=n;i++){
		if(vis[i])putchar('B');
		else putchar('W');
	}
	puts("");
	for(int i=1;i<=m;i++)printf("%d\n",ans[i]);
	return 0;
}