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 maxn = 2e5 + 5, inf = 1e9;
int n, m;
int d[maxn], a[maxn], b[maxn], c[maxn];
map<pair<int, int>, int> mp;
vector<int> G[maxn];
int main() {
	scanf("%d%d", &n, &m);
	for(int i = 1; i <= n; ++i) {
		scanf("%d", &d[i]);
	}
	for(int i = 1; i <= m; ++i) {
		scanf("%d%d", &a[i], &b[i]);
		G[a[i]].push_back(b[i]);
		G[b[i]].push_back(a[i]);
	}
	vector<pair<int, int> > v;
	for(int i = 1; i <= n; ++i) {
		v.emplace_back(d[i], i);
	}
	sort(v.begin(), v.end());
	for(int i = 0; i < v.size(); ++i) {
		int u = v[i].second;
		int p = 0;
		if(c[u]) {
			continue;
		}
		for(auto v : G[u]) {
			if(d[v] <= d[u]) {
				p = v;
				break;
			}
		}
		if(!p) {
			puts("-1");
			return 0;
		}
		if(!c[p]) {
			c[p] = 1;
		}	
		c[u] = -c[p];
		mp[minmax(u, p)] = d[u];
	}
	for(int i = 1; i <= n; ++i) {
		putchar(c[i] == 1 ? 'B' : 'W');
	}
	puts("");
	for(int i = 1; i <= m; ++i) {
		printf("%d\n", mp.count(minmax(a[i], b[i])) ? mp[minmax(a[i], b[i])] : inf);
	}
	return 0;
}