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;
typedef vector<int> vi;
typedef pair<int,int> pii;
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define sz(a) int(a.size())
const int N=2e5+10;

int gi() {
	int x=0,o=1;char ch=getchar();
	while((ch<'0'||ch>'9')&&ch!='-') ch=getchar();
	if(ch=='-') o=-1,ch=getchar();
	while(ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
	return x*o;
}

int n,to[N<<1],nxt[N<<1],d[N],ww[N<<1],tt=1,col[N],h[N],m;
bool vis[N];

void adde(int u,int v) {
	to[++tt]=v;nxt[tt]=h[u];h[u]=tt;
	to[++tt]=u;nxt[tt]=h[v];h[v]=tt;
}

void dfs(int u,int c=0) {
	col[u]=c;vis[u]=1;
	for(int i=h[u],v;v=to[i],i;i=nxt[i])
		if(~ww[i]&&!vis[v]) dfs(v,c^1);
}

int main() {
	memset(ww,-1,sizeof(ww));
	cin>>n>>m;
	for(int i=1;i<=n;i++) d[i]=gi();
	for(int i=1,u,v;i<=m;i++) u=gi(),v=gi(),adde(u,v);
	for(int u=1;u<=n;u++) {
		pii mn=mp(2e9,0);int e=0;
		for(int i=h[u],v;v=to[i],i;i=nxt[i])
			if(mp(d[v],v)<mn) mn=mp(d[v],v),e=i>>1;
		if(mn.fi>d[u]) return cout<<-1,0;
		if(e) ww[e<<1]=ww[e<<1|1]=d[u];
	}
	for(int i=1;i<=n;i++) if(!vis[i]) dfs(i);
	for(int i=1;i<=n;i++) putchar(col[i]?'W':'B');
	cout<<'\n';
	for(int i=1;i<=m;i++) {
		if(!~ww[i<<1]) ww[i<<1]=1e9;
		cout<<ww[i<<1]<<'\n';
	}
	return 0;
}