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 LL;

const int N=100000,M=200000,INF=1000000000;

int n,m,d[N+9];
struct side{
  int y,next,ans;
}e[M*2+9];
int lin[N+9],cs;

void Ins(int x,int y){e[++cs].y=y;e[cs].next=lin[x];lin[x]=cs;}
void Ins2(int x,int y){Ins(x,y);Ins(y,x);}

void into(){
  scanf("%d%d",&n,&m);
  cs=1;
  for (int i=1;i<=n;++i)
	scanf("%d",&d[i]);
  for (int i=1;i<=m;++i){
	int x,y;
	scanf("%d%d",&x,&y);
	Ins2(x,y);
  }
}

int ans[N+9],vis[N+9];

void Dfs_ans(int k,int c){
  ans[k]=c;
  vis[k]=1;
  for (int i=lin[k];i;i=e[i].next)
	if (!vis[e[i].y]&&e[i].ans) Dfs_ans(e[i].y,c^d[k]==d[e[i].y]);
}

void Get_ans(){
  for (int i=1;i<=n;++i){
	int mn=lin[i];
	for (int j=lin[i];j;j=e[j].next)
	  if (d[e[j].y]<d[e[mn].y]) mn=j;
    if (d[i]<d[e[mn].y]) {ans[0]=-1;return;}
	e[mn].ans=e[mn^1].ans=d[i]==d[e[mn].y]?d[i]:d[i]-d[e[mn].y];
  }
  for (int i=1;i<=n;++i)
	if (!vis[i]) Dfs_ans(i,0);
}

void work(){
  Get_ans();
}

void outo(){
  if (ans[0]==-1) puts("-1");
  else{
	for (int i=1;i<=n;++i)
	  putchar(ans[i]?'B':'W');
	puts("");
	for (int i=2;i<=m<<1;i+=2)
	  printf("%d\n",e[i].ans?e[i].ans:INF);
	puts("");
  }
}

int main(){
  into();
  work();
  outo();
  return 0;
}