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;

#define fi first
#define se second

#define N 100005

int n, m, D[N], id[N], d[N*2];

int col[N];

using pii = pair <int, int>;

vector <pii> v[N];

bool vis[N];

int main() {
	scanf("%d %d", &n, &m);
	for (int i = 1; i <= n; i ++) scanf("%d", &D[i]), id[i] = i;
	for (int i = 1, x, y; i <= m; i ++) {
		scanf("%d %d", &x, &y);
		v[x].emplace_back(y, i);
		v[y].emplace_back(x, i);
	}
	sort(id+1, id+n+1, [](int x, int y) {return D[x] < D[y];});
	for (int i = 1; i <= n; i ++) {
		int u = id[i];
		if (vis[u]) continue;
		bool flag = 0;
		for (auto x : v[u]) if (vis[x.fi]) {
			d[x.se] = D[u];
			col[u] = col[x.fi] ^ 1;
			flag = 1;
			vis[u] = 1;
			break;
		}
		if (flag) continue;
		for (auto x : v[u]) if (D[x.fi] == D[u]) {
			d[x.se] = D[u];
			vis[u] = vis[x.fi] = 1;
			col[u] = 1, col[x.fi] = 0;
			flag = 1;
			break;
		}
		if (!flag) {
			puts("-1");
			return 0;
		}
	}
	for (int i = 1; i <= n; i ++) printf("%c", "BW"[col[i]]);
	puts("");
	for (int i = 1; i <= m; i ++) {
		if (d[i] == 0) d[i] = 1e9;
		printf("%d\n", d[i]);
	}
	return 0;
}