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>
using namespace std;
#define LL long long
#define ULL unsigned long long
#define mp make_pair
#define pb push_back
#define pii pair<int,int>
#define pll pair<LL,LL>
#define x first
#define y second
#define pi acos(-1)
#define sqr(x) ((x)*(x))
#define pdd pair<double,double>
#define MEMS(x) memset(x,-1,sizeof(x))
#define MEM(x) memset(x,0,sizeof(x))
#define less Less
#define EPS 1e-4
#define arg ARG
#define cpdd const pdd
#define rank Rank
vector<pii> v[100005];
int val[200005];
int color[200005];
int d[100005];
void dfs(int x,int op=0){
    
    if(color[x]!=-1)return;
   // printf("%d %d\n",x,op);
    for(auto it:v[x]){
        if(d[it.x]<d[x]){
            dfs(it.x);
            color[x]=color[it.x];
            val[it.y]=d[x]-d[it.x];
            return ;
        }
        if(d[it.x]==d[x]&&op==0){
         //   printf("%d %d\n",x,it.x);
            dfs(it.x,1);
            if(color[it.x]==-1)color[it.x]=0,color[x]=1;
            else color[x]=color[it.x]^1;
            val[it.y]=d[it.x];
            return ;
        }
    }
}
int main(){
    int n,m;
    scanf("%d %d",&n,&m);
    for(int i = 1;i<=n;i++)
        scanf("%d",&d[i]);
    for(int i =  0;i<m;i++){
        int x,y;
        scanf("%d %d",&x,&y);
        v[x].pb(mp(y,i));
        v[y].pb(mp(x,i));
    }
    for(int i = 1;i<=n;i++){
        int Min=1e9;
        for(auto it:v[i]){
            //if(d[it.x])
            Min=min(Min,d[it.x]);
        }
       // printf("%d\n",i);
        if(Min>d[i]){
            printf("-1\n");
            return 0;
        }
    }
    fill(val,val+m,1e9);
    MEMS(color);
    for(int i =1;i<=n;i++){
        dfs(i);
    }
    for(int i = 1;i<=n;i++){
       // printf("%d\n",color[i]);
        printf("%c","BW"[color[i]]);
    }
    printf("\n");
    for(int i = 0;i<m;i++)
        printf("%d\n",val[i]);
}
/*
2 6
5 7
7 5
4 3
6 4
7 3
6 5
5 7
3 6
4 7
*/
//a+a+1=10a+1
//3a+2=10a+2