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 pb push_back
#define mp make_pair
#define fi first
#define se second
#define SZ(x) ((int)x.size())
#define FOR(i,a,b) for (int i=a;i<=b;++i)
#define FORD(i,a,b) for (int i=a;i>=b;--i)
using namespace std;
typedef long long LL;
typedef pair<int,int> pa;
typedef vector<int> vec;
void getint(int &v){
    char ch,fu=0;
    for(ch='*'; (ch<'0'||ch>'9')&&ch!='-'; ch=getchar());
    if(ch=='-') fu=1, ch=getchar();
    for(v=0; ch>='0'&&ch<='9'; ch=getchar()) v=v*10+ch-'0';
    if(fu) v=-v;
}
int d[500010],n,m,c[500010],p[500010],e[500010],x[500010],y[500010];
bool ok[500010];
bool cmp(int A,int B){
	return (d[y[A]]<d[y[B]] || d[y[A]]==d[y[B]] && d[x[A]]<d[x[B]]);
}
int main(){
	cin>>n>>m;
	FOR(i,1,n) getint(d[i]);
	FOR(i,1,m){
		getint(x[i]),getint(y[i]);
		if (d[x[i]]>d[y[i]]) swap(x[i],y[i]);
		if (d[y[i]]<=d[x[i]]) ok[x[i]]=1;
		if (d[x[i]]<=d[y[i]]) ok[y[i]]=1;
	}
	FOR(i,1,n) if (!ok[i]) return puts("-1"),0;
	FOR(i,1,m) p[i]=i;
	sort(p+1,p+m+1,cmp);
	memset(c,-1,sizeof(c));
	FOR(i,1,m){
		int h=p[i];
		if (c[x[h]]==-1 && c[y[h]]==-1){
			c[x[h]]=0;
			c[y[h]]=1;
		}
		else if (c[x[h]]==-1)
			c[x[h]]=c[y[h]]^1;
		else if (c[y[h]]==-1)
			c[y[h]]=c[x[h]]^1;
		e[h]=max(d[x[h]],d[y[h]]);
	}
	FOR(i,1,n) if (c[i]==0) putchar('W'); else putchar('B');
	puts("");
	FOR(i,1,m) printf("%d\n",e[i]);
	return 0;
}