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 mp make_pair
using namespace std;
const int maxn=1e5+10;
int n,m;
int d[maxn],w[maxn*2],col[maxn];
vector<pair<int,int> > G[maxn];

void solve(){
    scanf("%d%d",&n,&m);
    for(int i=0;i<n;++i){
        scanf("%d",d+i);
    }
    for(int i=0,u,v;i<m;++i){
        scanf("%d%d",&u,&v);
        --u;--v;
        G[u].push_back(mp(v,i));
        G[v].push_back(mp(u,i));
    }

    map<int,vector<int> > mp;
    memset(col,-1,sizeof col);
    for(int i=0;i<n;++i)mp[d[i]].push_back(i);

    for(auto &e: mp){
        for(auto u: e.second)if(!~col[u]){
            for(auto nxt: G[u]){
                if(d[nxt.first]<=d[u]){
                    w[nxt.second]=e.first;
                    if(col[nxt.first]==-1){
                        col[u]=0;
                        col[nxt.first]=1;
                    }
                    else col[u]=col[nxt.first]^1;
                    goto H;
                }
            }
            puts("-1");
            return;
            H:;
        }
    }
    for(int i=0;i<n;++i)
        putchar(col[i]?'B':'W');

    for(int i=0;i<m;++i){
        printf("\n%d",w[i]?w[i]:1000000000);
    }
}
int main(){
    solve();

    return 0;
}