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;

const int _ = 2e5 + 7;
struct Edge{int end , id , upEd;}Ed[_ << 1];
int head[_] , N , M , val[_] , D[_] , col[_] , cntEd;
void addEd(int a , int b , int c){Ed[++cntEd] = (Edge){b , c , head[a]}; head[a] = cntEd;}
int fa[_] , sz[_]; bool vis[_];
int find(int x){return fa[x] == x ? x : (fa[x] = find(fa[x]));}
void dfs(int x , int p , int c){
	col[x] = c; vis[x] = 1;
	for(int i = head[x] ; i ; i = Ed[i].upEd)
		if(Ed[i].end != p)
			if(D[Ed[i].end] == D[x] && !vis[Ed[i].end]){dfs(Ed[i].end , x , c ^ 1); val[Ed[i].id] = D[x];}
			else if(D[Ed[i].end] <= D[x]) val[Ed[i].id] = 1e9;
}

int main(){
	cin >> N >> M; for(int i = 1 ; i <= N ; ++i) cin >> D[i];
	for(int i = 1 ; i <= M ; ++i){int s , t; cin >> s >> t; addEd(s , t , i); addEd(t , s , i);}
	vector < int > pos; for(int i = 1 ; i <= N ; ++i) pos.push_back(i);
	sort(pos.begin() , pos.end() , [&](int x , int y){return D[x] < D[y];});
	for(int i = 0 , pi ; i < N ; i = pi){
		pi = i; while(pi < N && D[pos[pi]] == D[pos[i]]){sz[fa[pos[pi]] = pos[pi]] = 1; ++pi;}
		for(int j = i ; j < pi ; ++j)
			for(int k = head[pos[j]] ; k ; k = Ed[k].upEd)
				if(D[Ed[k].end] == D[pos[j]] && find(Ed[k].end) != find(pos[j])){
					sz[find(pos[j])] += sz[find(Ed[k].end)]; fa[find(Ed[k].end)] = find(pos[j]);
				}
		for(int j = i ; j < pi ; ++j)
			if(fa[pos[j]] == pos[j])
				if(sz[pos[j]] > 1) dfs(pos[j] , 0 , 0);
				else{
					bool flg = 0;
					for(int k = head[pos[j]] ; k ; k = Ed[k].upEd)
						if(D[Ed[k].end] < D[pos[j]])
							if(!flg){col[pos[j]] = col[Ed[k].end]; val[Ed[k].id] = D[pos[j]] - D[Ed[k].end]; flg = 1;}
							else val[Ed[k].id] = 1e9;
					if(!flg){puts("-1"); return 0;}
				}
	}
	for(int i = 1 ; i <= N ; ++i) putchar(col[i] ? 'W' : 'B');
	cout << endl; for(int i = 1 ; i <= M ; ++i) cout << val[i] << endl;
	return 0;
}