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 <cstring>
#define il inline
#define ri register
#define Size 800050
using namespace std;
int D[Size];
struct graph{
	struct point{
		int next,to;
	}ar[Size];
	int head[Size],art=1;
	il void link(int u,int v){
		ar[++art]={head[u],v},head[u]=art;
		ar[++art]={head[v],u},head[v]=art;
	}
}G,G1;
int ans[Size],a[Size];
il void read(int&),dfs(int,bool);
int main(){
	//freopen("in","r",stdin);
	int N,M;read(N),read(M);
	for(int i(1);i<=N;++i)read(D[i]);
	for(int i(1),u,v;i<=M;++i)
		read(u),read(v),G.link(u,v),ans[i]=1e9;
	for(int i(1),j,i1;i<=N;++i){
		for(j=G.head[i],i1=0;j;j=G.ar[j].next)
			if(!i1||make_pair(D[G.ar[j].to],G.ar[j].to)<
			   make_pair(D[G.ar[i1].to],G.ar[i1].to))i1=j;
		if(D[G.ar[i1].to]>D[i])return puts("-1"),0;
		ans[i1>>1]=D[i],G1.link(i,G.ar[i1].to);
	}memset(a,-1,sizeof(a));
	for(int i(1);i<=N;++i)if(!~a[i])dfs(i,0);
	for(int i(1);i<=N;++i)putchar(a[i]?'B':'W');
	putchar('\n');
	for(int i(1);i<=M;++i)printf("%d\n",ans[i]);
	return 0;
}
il void dfs(int x,bool c){a[x]=c;
	for(int i(G1.head[x]),i1;i;i=G1.ar[i].next)
		if(!~a[i1=G1.ar[i].to])dfs(i1,c^1);
}
il void read(int&x){
	x^=x;ri char c;while(c=getchar(),c<'0'||c>'9');
	while(c>='0'&&c<='9')x=(x<<1)+(x<<3)+(c^48),c=getchar();
}