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;

typedef long long lint;
typedef long double louble;

template<typename T1,typename T2> inline T1 max(T1 a,T2 b){return a<b?b:a;}
template<typename T1,typename T2> inline T1 min(T1 a,T2 b){return a<b?a:b;}

const char lf = '\n';

namespace ae86
{
	const int bufl = 1 << 15;

	char buf[bufl],*s=buf,*t=buf;

	inline int fetch()
	{
		if(s==t){t=(s=buf)+fread(buf,1,bufl,stdin);if(s==t)return EOF;}
		return *s++;
	}

	inline int ty()
	{
		int a=0,b=1,c=fetch();
		while(!isdigit(c))b^=c=='-',c=fetch();
		while(isdigit(c))a=a*10+c-48,c=fetch();
		return a;
	}
}
using ae86::ty;

const int _ = 100007 , __ = 200007 , inf = 1e9;
const int _e = __ << 1;

int to[_e],ne[_e],ev[_e],he[_]={0},ecnt=1;
inline void adde(int a,int b,int c){to[++ecnt]=b,ev[ecnt]=c,ne[ecnt]=he[a],he[a]=ecnt;}
inline void addde(int a,int b,int c){adde(a,b,c),adde(b,a,c);}

int n,m,ned[_]={0},ea[__],eb[__],eva[__]={0};
int col[_]={0};

struct cxk
{
	int x,d;
	cxk(int x_=0,int d_=0){x=x_,d=d_;}
	friend bool operator < (cxk a,cxk b){return a.d<b.d;}
};
priority_queue<cxk> dlq;

void failure()
{
	cout<<-1<<lf;
	exit(0);
}

int main()
{
	ios::sync_with_stdio(0),cout.tie(nullptr);

	n=ty(),m=ty();
	for(int i=1;i<=n;i++)ned[i]=ty();
	for(int i=1;i<=m;i++)ea[i]=ty(),eb[i]=ty(),addde(ea[i],eb[i],i);

	int got=0,spc=0;
	for(int i=1;i<=m;i++)
	{
		int a=ea[i],b=eb[i];
		if(ned[a]==ned[b] && !col[a] && !col[b])
		{
			dlq.emplace(a,ned[a]),dlq.emplace(b,ned[b]);
			col[a]=1,col[b]=2,spc+=2;
			eva[i]=ned[a],got=1;
		}
	}

	if(!got)failure();

	while(!dlq.empty())
	{
		int a=dlq.top().x;dlq.pop();
		for(int i=he[a];i;i=ne[i])
		{
			int b=to[i];
			if(col[b] || ned[b]<ned[a])continue;
			col[b]=3-col[a],eva[ev[i]]=ned[b],spc++;
			dlq.emplace(b,ned[b]);
		}
	}

	if(spc<n)failure();
	for(int i=1;i<=n;i++)cout<<"BW"[col[i]-1];
	cout<<lf;
	for(int i=1;i<=m;i++)
	{
		if(!eva[i])eva[i]=inf;
		cout<<eva[i]<<lf;
	}

	return 0;
}