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;
#define ll long long
#define REP(i,a,b) for(int i=(a),_end_=(b);i<=_end_;i++)
#define DREP(i,a,b) for(int i=(a),_end_=(b);i>=_end_;i--)
#define EREP(i,u) for(int i=start[u];i;i=e[i].next)
#define fi first
#define se second
#define mkr(a,b) make_pair(a,b)
#define SZ(A) ((int)A.size())
template<class T>inline void chkmin(T &a,T b){ if(a>b)a=b;}
template<class T>inline void chkmax(T &a,T b){ if(a<b)a=b;}
inline int read()
{
	int s=0,f=1; char ch=getchar();
	while(!isdigit(ch) && ch!='-')ch=getchar();
	if(ch=='-')ch=getchar(),f=-1;
	while(isdigit(ch))s=s*10+ch-'0',ch=getchar();
	return ~f?s:-s;
}

const int inf=1e9;
const int maxn=2e5+20;

struct Edge {
	int u,v,w;
};
Edge E[maxn];

int d[maxn],n,m,vis[maxn],col[maxn];
vector<int>ed[maxn];
queue<int>q;

inline void init()
{
	n=read();m=read();
	REP(i,1,n)d[i]=read();
	REP(i,1,m)
	{
		int u=read(),v=read();
		E[i]=(Edge){u,v,inf};
		if(d[u]==d[v] && !vis[u] && !vis[v])
			q.push(u),q.push(v),E[i].w=d[u],vis[u]=1,vis[v]=1,col[u]=1,col[v]=0;
		ed[u].push_back(i);
		ed[v].push_back(i);
	}
}

inline void doing()
{
	while(!q.empty())
	{
		int u=q.front();q.pop();
		for(int i:ed[u])
		{
			int v=E[i].u^E[i].v^u;
			if(d[v]>=d[u] && !vis[v])
				vis[v]=1,q.push(v),E[i].w=d[v],col[v]=col[u]^1;
		}
	}
	int s=0;
	REP(i,1,n)s+=vis[i];
	if(s==n)
	{
		REP(i,1,n)printf("%c",col[i]?'B':'W'); puts("");
		REP(i,1,m)printf("%d\n",E[i].w);
	}else puts("-1");
}

int main()
{
	init();
	doing();
	return 0;
}