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<cstdio>
#include<cmath>
#include<algorithm>
#include<cstdlib>
#include<cstring>
using namespace std;
inline int read()
{
	int x=0,f=1;char ch=getchar();
	while(ch<'0' || ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0' && ch<='9')x=x*10+ch-'0',ch=getchar();
	return x*f;
}
int stack[20];
inline void write(int x)
{
	if(x<0){putchar('-');x=-x;}
	if(!x){putchar('0');return;}
	int top=0;
	while(x)stack[++top]=x%10,x/=10;
	while(top)putchar(stack[top--]+'0');
}
inline void pr1(int x){write(x),putchar(' ');}
inline void pr2(int x){write(x),puts("");}
struct node
{
	int x,y,c,next;
}a[400010];int len,last[100010];
inline void ins(int x,int y,int c)
{
	len++;
	a[len].x=x;a[len].y=y;a[len].c=c;
	a[len].next=last[x];last[x]=len;
}
int d[100010],p[100010];
bool cmp(int x,int y){return d[x]<d[y];}
int id[100010],e[200010];
int main()
{
	//freopen("a.in","r",stdin);
	//freopen("a.out","w",stdout);
	int n=read(),m=read();
	for(int i=1;i<=n;i++)d[i]=read(),p[i]=i;
	for(int i=1;i<=m;i++)
	{
		int x=read(),y=read();
		ins(x,y,i),ins(y,x,i);
	}sort(p+1,p+n+1,cmp);
	for(int i=1;i<=n;i++)
	{
		int x=p[i];
		for(int k=last[x];k;k=a[k].next)
		{
			int y=a[k].y;
			if(d[y]==d[x])
			{
				e[a[k].c]=d[x];
				if(!id[y])
				{
					if(id[x])id[y]=3-id[x];
					else id[x]=1,id[y]=2;
				}
				else if(!id[x])id[x]=3-id[y];
			}
			else if(d[y]<d[x])
			{
				if(!id[x])id[x]=id[y],e[a[k].c]=d[x]-d[y];
				else e[a[k].c]=d[x];
			}
		}
	}
	bool bk=true;
	for(int i=1;i<=n;i++)if(!id[i]){bk=false;break;}
	if(bk==false)puts("-1");
	else
	{
		for(int i=1;i<=n;i++)
		{
			if(id[i]==1)putchar('B');
			else putchar('W');
		}puts("");
		for(int i=1;i<=m;i++)pr2(e[i]);
	}
	return 0;
}