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;
const int N = 5e5 + 5;
int n, m, tot, c[N], a[N], head[N], nex[N], to[N], id[N];
void add(int u, int v, int i) {to[++tot] = v; nex[tot] = head[u]; head[u] = tot; id[tot] = i;}
bool vis[N];
int dis[N];
int ans;
struct node
{
	int u, x;
	node(int u = 0, int x = 0): u(u), x(x) {}
	bool operator<(const node&o)const
	{
		return x < o.x;
	}
};
priority_queue<node>q;
int main()
{
	scanf("%d%d", &n, &m);
	for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
	bool flag = false;
	for (int i = 1; i <= m; i++)
	{
		int u, v; scanf("%d%d", &u, &v);
		add(u, v, i); add(v, u, i);
		if (a[u] == a[v] && !vis[u] && !vis[v])
		{
			q.push(node(u, a[u]));
			q.push(node(v, a[v]));
			c[u] = 1; c[v] = 0;
			vis[u] = vis[v] = true;
			ans += 2;
			dis[i] = a[u];
			flag = true;
		}
	}
	if (!flag) {printf("-1\n"); return 0;}
	while (!q.empty())
	{
		node now = q.top(); q.pop();
		for (int i = head[now.u]; i; i = nex[i])
		{
			int v = to[i]; if (vis[v] || a[v] < now.x) continue;
			vis[v] = true; ans++;
			dis[id[i]] = a[v];
			c[v] = c[now.u] ^ 1;
			q.push(node(v, a[v]));
		}
	}
	if (ans != n) {printf("-1\n"); return 0;}
	for (int i = 1; i <= n; i++)
		putchar(c[i] ? 'B' : 'W');
	putchar('\n');
	for (int i = 1; i <= m; i++)
		printf("%d\n", !dis[i] ? 1000000000 : dis[i]);
}