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 SIZE 200005
#define INF 1000000000
using namespace std;
typedef long long int ll;
typedef pair <int,int> P;

int D[SIZE];
vector <P> vec[SIZE];
int ans[SIZE],col[SIZE];
bool act[SIZE];
int main()
{
	int n,m;
	scanf("%d %d",&n,&m);
	for(int i=0;i<n;i++) scanf("%d",&D[i]);
	for(int i=0;i<m;i++)
	{
		int a,b;
		scanf("%d %d",&a,&b);a--,b--;
		vec[a].push_back(P(b,i));
		vec[b].push_back(P(a,i));
	}
	for(int i=0;i<n;i++)
	{
		bool up=false;
		for(int j=0;j<vec[i].size();j++)
		{
			int to=vec[i][j].first;
			if(D[to]<=D[i]) up=true;
		}
		if(!up)
		{
			puts("-1");
			return 0;
		}
	}
	vector <P> vx;
	for(int i=0;i<n;i++) vx.push_back(P(D[i],i));
	sort(vx.begin(),vx.end());
	memset(col,-1,sizeof(col));
	for(int i=0;i<n;i++)
	{
		int v=vx[i].second;
		//printf("* %d\n",v);
		act[v]=true;
		bool up=false;
		for(int j=0;j<vec[v].size();j++)
		{
			int to=vec[v][j].first;
			if(act[to])
			{
				if(D[to]==D[v])
				{
					//printf("* %d %d\n",to,vec[v][j].second);
					up=true;
					if(col[to]==-1)
					{
						if(col[v]!=-1) col[to]=1-col[v];
						else col[to]=0,col[v]=1;
					}
					else if(col[v]==-1) col[v]=1-col[to];
					ans[vec[v][j].second]=D[v];
				}
			}
		}
		if(up)
		{
			for(int j=0;j<vec[v].size();j++)
			{
				int to=vec[v][j].first;
				if(act[to]&&D[to]<D[v]) ans[vec[v][j].second]=INF;
			}
		}
		else
		{
			for(int j=0;j<vec[v].size();j++)
			{
				int to=vec[v][j].first;
				if(act[to])
				{
					if(col[v]==-1) col[v]=col[to],ans[vec[v][j].second]=D[v]-D[to];
					else ans[vec[v][j].second]=INF;
				}
			}
		}
	}
	for(int i=0;i<n;i++) printf("%c",col[i]==0?'B':'W');
	puts("");
	for(int i=0;i<m;i++) printf("%d\n",ans[i]);
	return 0;
}