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 llong long long
#define mkpr make_pair
#define x first
#define y second
#define iter iterator
#define riter reversed_iterator
#define y1 Lorem_ipsum_
#define tm dolor_sit_amet_
using namespace std;

inline int read()
{
	int x = 0,f = 1; char ch = getchar();
	for(;!isdigit(ch);ch=getchar()) {if(ch=='-') f = -1;}
	for(; isdigit(ch);ch=getchar()) {x = x*10+ch-48;}
	return x*f;
}

const int mxN = 1e5;
const int mxM = 2e5;
const int INF = 1e9;
struct Edge
{
	int v,nxt,id;
} e[mxM*2+3];
int w[mxM+3];
int fe[mxN+3];
int d[mxN+3];
int mn[mxN+3];
bool vis[mxN+3];
int p[mxN+3],pi[mxN+3];
int c[mxN+3];
int n,m,en;

void addedge(int u,int v,int id)
{
	en++; e[en].v = v; e[en].id = id;
	e[en].nxt = fe[u]; fe[u] = en;
}

bool cmp_d(int x,int y) {return d[x]<d[y];}

int main()
{
	n = read(),m = read();
	for(int i=1; i<=n; i++) d[i] = read();
	for(int i=1; i<=m; i++) {int u = read(),v = read(); addedge(u,v,i),addedge(v,u,i);}
	bool ok = true;
	for(int i=1; i<=n; i++)
	{
		mn[i] = INF;
		for(int o=fe[i]; o; o=e[o].nxt)
		{
			mn[i] = min(mn[i],d[e[o].v]);
		}
		if(mn[i]>d[i]) {ok = false; break;}
	}
	if(!ok) {puts("-1"); return 0;}
	for(int i=1; i<=n; i++) p[i] = i;
	sort(p+1,p+n+1,cmp_d);
	for(int i=1; i<=m; i++) w[i] = INF;
	for(int i=1; i<=n; i++)
	{
		int u = p[i]; bool found = false;
		if(vis[u]) continue;
		for(int o=fe[u]; o; o=e[o].nxt)
		{
			int v = e[o].v;
			if(vis[v])
			{
				c[u] = c[v]^1;
				w[e[o].id] = d[u];
				vis[u] = true;
				found = true; break;
			}
		}
		if(found) continue;
		for(int o=fe[u]; o; o=e[o].nxt)
		{
			int v = e[o].v;
			if(d[v]==d[u])
			{
				c[u] = 0,c[v] = 1;
				w[e[o].id] = d[u];
				vis[u] = vis[v] = true;
				found = true; break;
			}
		}
		assert(found);
	}
	for(int i=1; i<=n; i++) printf("%c",c[i]?'W':'B'); puts("");
	for(int i=1; i<=m; i++) printf("%d\n",w[i]);
	return 0;
}