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 <sstream>
#include <fstream>
#include <string>
#include <vector>
#include <deque>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <algorithm>
#include <functional>
#include <utility>
#include <bitset>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <cstdio>

using namespace std;

const int MAXN = 200001;
int n,m,d[MAXN],col[MAXN],ans[MAXN],good[MAXN];
vector<pair<int,int>> adj[MAXN];

void dfs(int s, int c){
    col[s]=c;
    for(auto t:adj[s]){
        if(col[t.first]==-1){
            ans[t.second]=d[t.first];
            dfs(t.first,c^1);
        }
    }
}

int main(){
    scanf("%d%d",&n,&m);
    for(int i=0;i<n;i++){
        scanf("%d",&d[i]);
        col[i]=-1;
    }
    for(int i=0;i<m;i++){
        int x,y;
        ans[i]=1e9;
        scanf("%d%d",&x,&y);x--;y--;
        if(d[x]==d[y]){
            good[x]=1;
            adj[x].push_back({y,i});
            adj[y].push_back({x,i});
        }
        else if(d[x]>d[y]){
            adj[y].push_back({x,i});
        }
        else {
            adj[x].push_back({y,i});
        }
    }
    for(int i=0;i<n;i++){
        if(good[i]&&col[i]==-1){
            dfs(i,0);
        }
    }
    for(int i=0;i<n;i++){
        if(col[i]==-1){
            cout << -1 << endl;
            return 0;
        }
    }
    for(int i=0;i<n;i++){
        cout<<"BW"[col[i]];
    }
    cout<<endl;
    for(int i=0;i<m;i++){
        printf("%d\n",ans[i]);
    }

}