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 <algorithm>
#include <vector>
#include <map>
#include <set>
using namespace std;
const int N=1000000+10;
int n,m,d[N];
vector<int> g[N];
pair<int,int> p[N];
map< pair<int,int>,int > id;
set<int> st;
int col[N],ans[N];
void dfs(int u){
    int cnt=0;
    for(auto v: g[u]) {
        if(st.count(v)) {
            if(col[v]==0){
                col[v]=3-col[u]; 
                ans[id[make_pair(u,v)]] = d[u]; cnt++;
                dfs(v);
            } else if (col[v]+col[u]==3) {
                cnt ++;
            }
            continue;
        }
        if(col[v]==3-col[u]) {
            ans[id[make_pair(u,v)]] = d[u]; cnt++;
        }
    }
    if(cnt==0) {
        printf("-1\n"); exit(0);
    }
}

int main(){
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++)scanf("%d",&d[i]),p[i]=make_pair(d[i],i);
    for(int i=1;i<=m;i++){
        int x,y; scanf("%d%d",&x,&y); 
        g[x].push_back(y); g[y].push_back(x);
        id[make_pair(x,y)]=id[make_pair(y,x)]=i;
    }
    sort(p+1,p+1+n);
    for(int i=1,j=1;i<=n;i=j){
        vector<int> tmp; st.clear();
        while(j<=n && p[j].first==p[i].first) {
            tmp.push_back(p[j].second); st.insert(p[j].second); j++;
        }
        //printf("!\n");
        for(auto x: tmp){
            //printf("%d ",x);
            if(col[x]==0){
                for(auto v: g[x]) {
                    if(col[v]) {
                        col[x]=3-col[v];
                    }
                } 
                if(!col[x]) col[x]=1; 
                dfs(x);
            }
        }
        //printf("\n");
    }
    for(int i=1;i<=n;i++){
        printf("%c", col[i]==1?'W':'B');
    }
    printf("\n");
    for(int i=1;i<=m;i++){
        printf("%d\n", ans[i]?ans[i]:(int)1e9);
    }
}