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 LL long long
#define uLL unsigned long long

using namespace std;
const int N=2e5+10,inf=1e9;
int rd()
{
    int x=0,w=1;char ch=0;
    while(ch<'0'||ch>'9'){if(ch=='-') w=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+(ch^48);ch=getchar();}
    return x*w;
}
int to[N<<1],nt[N<<1],hd[N],tot=1;
void adde(int x,int y)
{
    ++tot,to[tot]=y,nt[tot]=hd[x],hd[x]=tot;
    ++tot,to[tot]=x,nt[tot]=hd[y],hd[y]=tot;
}
char co[2]={'W','B'};
int n,m,a[N],sq[N],a1[N],a2[N];
bool cmp(int aa,int bb){return a[aa]<a[bb];}

int main()
{
//orz itst
    n=rd(),m=rd();
    for(int i=1;i<=n;++i) a[i]=rd();
    for(int i=1;i<=m;++i) adde(rd(),rd());
    for(int i=1;i<=max(n,m);++i) a1[i]=-1,a2[i]=inf+1;
    for(int i=1;i<=n;++i) sq[i]=i;
    sort(sq+1,sq+n+1,cmp);
    for(int i=1;i<=n;++i)
    {
	int x=sq[i];
	for(int j=hd[x];j;j=nt[j])
	{
	    int y=to[j];
	    if(a[y]>a[x]||((~a1[x])&&(~a1[y]))) continue;
	    if(a[x]==a[y])
	    {
		a2[j>>1]=a[x];
		if(a1[x]<0)
		{
		    if(a1[y]<0) a1[y]=0;
		    a1[x]=a1[y]^1;
		}
		else a1[y]=a1[x]^1;
	    }
	    else if(~a1[y])
		a2[j>>1]=a[x]-a[y],a1[x]=a1[y];
	}
    }
    for(int i=1;i<=n;++i)
	if(a1[i]<0){puts("-1");return 0;}
    for(int i=1;i<=n;++i) putchar(co[a1[i]]);
    puts("");
    for(int i=1;i<=m;++i) printf("%d\n",min(a2[i],inf));
    return 0;
}