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>

#ifdef NON_SUBMIT
#define TEST(n) (n)
#define tout cerr
#else
#define TEST(n) ((void)0)
#define tout cin
#endif

using namespace std;

vector<pair<int,int>> adj[100000];
vector<int> tree[100000];
vector<tuple<int,int,int>> E;
bool used[100000];
string ans;
int V[100000], res[200000], color[100000];

int find_(int a)
{
	return color[a]=color[a]==a ? a:find_(color[a]);
}

void union_(int a, int b)
{
	color[find_(a)]=find_(b);
}

void dfs(int c, int v)
{
	used[c]=false;
	ans[c]=v ? 'B':'W';
	for(auto n: tree[c]) if(used[n]) dfs(n,!v);
}

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(NULL); cout.tie(NULL);
	TEST(freopen("input.txt","r",stdin));
	TEST(freopen("output.txt","w",stdout));
	TEST(freopen("debug.txt","w",stderr));
	int N, M, tot=0;
	queue<int> Q;
	cin>>N>>M;
	for(int i=0;i<N;i++) {
		cin>>V[i];
		color[i]=i;
	}
	for(int i=0;i<M;i++) {
		int a, b;
		cin>>a>>b;
		adj[--a].emplace_back(--b,i);
		adj[b].emplace_back(a,i);
		if(V[a]==V[b]) {
			res[i]=V[a];
			if(!used[a]) {
				used[a]=true;
				Q.push(a);
			}
			if(!used[b]) {
				used[b]=true;
				Q.push(b);
			}
			if(find_(a)!=find_(b)) {
				union_(a,b);
				tree[a].push_back(b);
				tree[b].push_back(a);
			}
		}
		else res[i]=1e9;
	}
	ans.resize(N);
	while(!Q.empty()) {
		int c=Q.front();
		Q.pop();
		tot++;
		for(auto n: adj[c]) if(V[n.first]>=V[c] && !used[n.first]) {
			if(find_(c)!=find_(n.first)) {
				union_(c,n.first);
				tree[c].push_back(n.first);
				tree[n.first].push_back(c);
			}
			used[n.first]=true;
			res[n.second]=V[n.first];
			Q.push(n.first);
		}
	}
	if(tot<N) {
		cout<<"-1\n";
		return 0;
	}
	for(int i=0;i<N;i++) if(used[i]) dfs(i,0);
	cout<<ans<<'\n';
	for(int i=0;i<M;i++) cout<<res[i]<<'\n';
	return 0;
}