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:
//@winlere
#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<queue>

using namespace std;  typedef long long ll;
inline int qr(){
	int ret=0,f=0,c=getchar();
	while(!isdigit(c)) f|=c==45,c=getchar();
	while( isdigit(c)) ret=ret*10+c-48,c=getchar();
	return f?-ret:ret;
}
const int maxn=1e5+5;
const int inf=1e9;
struct E{
	int to,nx;
}e[maxn<<2];
int head[maxn],ans[maxn<<1],usd[maxn],n,m,cnt,D[maxn];
char col[maxn];
void add(int fr, int to){
	static int cnt=1;
	e[++cnt]=(E){to,head[fr]}; head[fr]=cnt;
	e[++cnt]=(E){fr,head[to]}; head[to]=cnt;
}
queue< int > q;

int main(){
	n=qr(); m=qr();
	for(int t=1;t<=n;++t)D[t]=qr();
	for(int t=1,a,b;t<=m;++t){
		a=qr(),b=qr(),add(a,b);
		if(D[a]==D[b]&&!col[a]&&!col[b]) q.emplace(a),q.emplace(b),col[a]='W',col[b]='B',ans[t]=D[a];
	}
	while(q.size()){
		int now=q.front(); q.pop();
		for(int t=head[now];t;t=e[t].nx)
			if(!col[e[t].to]&&D[e[t].to]>=D[now])
				col[e[t].to]="WB"[col[now]=='W'],ans[t>>1]=D[e[t].to],q.emplace(e[t].to);
	}
	for(int t=1;t<=n;++t)
		if(col[t]==0)
			return puts("-1"),0;
	puts(col+1);
	for(int t=1;t<=m;++t)
		printf("%d\n",ans[t]?ans[t]:inf);
	return 0;
}