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 ll long long
#define ull unsigned ll
#define uint unsigned
#define pii pair<int,int>
#define pll pair<ll,ll>
#define IT iterator
#define PB push_back
#define fi first
#define se second
#define For(i,j,k) for (int i=(int)(j);i<=(int)(k);i++)
#define Rep(i,j,k) for (int i=(int)(j);i>=(int)(k);i--)
#define CLR(a,v) memset(a,v,sizeof(a));
#define CPY(a,b) memcpy(a,b,sizeof(a));
#define debug puts("wzpakking")
#define y1 ysghysgsygsh
using namespace std;
const int N=500005;
int n,m,v1[N],x[N],y[N],co[N],ans[N];
pii v2[N];
vector<int> e[N];
void color(int x){
	for (auto i:e[x]) if (!co[i])
		co[i]=co[x]^3,color(i);
}
int main(){
	scanf("%d%d",&n,&m);
	For(i,1,n){
		scanf("%d",&v1[i]);
		v2[i].fi=1ll<<30;
	}
	For(i,1,m){
		scanf("%d%d",&x[i],&y[i]);
		v2[y[i]]=min(v2[y[i]],pii(v1[x[i]],i));
		v2[x[i]]=min(v2[x[i]],pii(v1[y[i]],i));
	}
	For(i,1,n) if (v2[i].fi>v1[i]) return puts("-1"),0;
	For(i,1,m) ans[i]=1000000000;
	For(i,1,n) ans[v2[i].se]=v1[i];
	For(i,1,n) e[x[v2[i].se]].PB(y[v2[i].se]);
	For(i,1,n) e[y[v2[i].se]].PB(x[v2[i].se]);
	For(i,1,n) if (co[i]==0) co[i]=1,color(i);
	For(i,1,n) putchar(co[i]==1?'B':'W');
	puts("");
	For(i,1,m) printf("%d\n",ans[i]);
}