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<cstdio>
#include<algorithm>
#include<cstring>
#include<vector>
#include<cassert>
using namespace std;
#define N 200020
inline int read(){
	int x=0,f=1;
	char c=getchar();
	while(c<'0'||c>'9'){
		if(c=='-')f=-1;
		c=getchar();
	}
	while(c>='0'&&c<='9'){
		x=(x<<1)+(x<<3)+c-'0';
		c=getchar();
	}
	return x*f;
}
int n,m,d[N],t[N],ans[N];
pair<int,int> p[N];
vector<pair<int,int> > G[N];
struct Union{
	int f[N];
	void init(int n){
		for(int i=1;i<=n;++i)f[i]=i;
	}
	inline int getf(int x){
		return f[x]==x?x:f[x]=getf(f[x]);
	}
}S;
int main(){
	n=read(),m=read();
	for(int i=1;i<=n;++i){
		d[i]=read();
		t[i]=-1;
	}
	for(int i=1;i<=m;++i){
		int u=read(),v=read();
		G[u].emplace_back(v,i);
		G[v].emplace_back(u,i);
		ans[i]=1e9;
	}
	for(int i=1;i<=n;++i){
		p[i]=(*min_element(G[i].begin(),G[i].end(),[&](pair<int,int> i,pair<int,int> j){
			return d[i.first]==d[j.first]?i.first<j.first:d[i.first]<d[j.first];
		}));
		if(d[p[i].first]>d[i]){
			return !printf("-1\n");
		}
	}
	for(int i=1;i<=n;++i){
		int u=p[i].first;
		if(~t[i])continue;
		if(d[u]==d[i]){
			if(~t[u]){
				t[i]=t[u]^1;
			}
			else{
				t[i]=0,t[u]=1;
			}
			ans[p[i].second]=d[i];
		}
	}
	S.init(n);
	for(int i=1;i<=n;++i){
		if(~t[i])continue;
		int u=p[i].first;
		S.f[i]=u;
		ans[p[i].second]=d[i]-d[u];
	}
	for(int i=1;i<=n;++i){
		putchar(t[S.getf(i)]?'B':'W');
	}
	putchar('\n');
	for(int i=1;i<=m;++i){
		printf("%d\n",ans[i]);
	}
	return 0;
}