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;
using pii = pair<int, int>;

bool chk[100009], bl[100009];
vector<pii> G[100009];
int D[100009], w[200009];

int main() {
	int N, M; scanf("%d%d",&N,&M);
	for(int i=1; i<=N; i++) scanf("%d", &D[i]);
	for(int i=0; i<M; i++) {
		int u, v; scanf("%d%d",&u,&v);
		G[u].push_back({v, i});
		G[v].push_back({u, i});
		w[i] = 1e9;
	}
	vector<int> S;
	for(int i=1; i<=N; i++) S.push_back(i);
	sort(S.begin(), S.end(), [&](int P, int Q) { return D[P] < D[Q]; });
	for(auto& it: S) {
		if(chk[it]) continue;
		chk[it] = 1;
		int nei = -1, id = -1;
		for(auto& jt: G[it]) if(chk[jt.first]) tie(nei, id) = jt;
		if(nei != -1) {
			w[id] = D[it];
			bl[it] = bl[nei] ^ 1;
		}
		else {
			for(auto& jt: G[it]) if(D[jt.first] == D[it]) tie(nei, id) = jt;
			if(nei != -1) {
				chk[nei] = 1;
				w[id] = D[it];
				bl[it] = 1;
			}
			else return !printf("-1");
		}
	}
	for(int i=1; i<=N; i++) {
		if(bl[i]) printf("B");
		else printf("W");
	}
	for(int i=0; i<M; i++) printf("\n%d", w[i]);
	return 0;
}