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 <cstdio>
#include <vector>
#include <queue>
#include <utility>
#include <string>
#include <algorithm>
using namespace std;

typedef pair<int,int> pii;

int main() try{
	const int INF = 1010101010;

	int n, m;
	scanf("%d%d", &n, &m);
	vector<int> ds(n + 1, INF);
	for(int i = 0; i < n; ++i){ scanf("%d", &ds[i]); }
	vector<vector<pii>> G(n);
	for(int i = 0; i < m; ++i){
		int a, b;
		scanf("%d%d", &a, &b);
		G[a - 1].emplace_back(b - 1, i);
		G[b - 1].emplace_back(a - 1, i);
	}

	string res1(n, '?');
	vector<int> res2(m, 1000000000);
	priority_queue<pii> pq;
	for(int i = 0; i < n; ++i){
		if(res1[i] != '?'){ continue; }
		int minadj = INF;
		pii pe(-1, -1);
		for(const pii &e : G[i]){
			int v = e.first;
			minadj = min(minadj, ds[v]);
			if(ds[v] == ds[i] && res1[v] == '?'){
				pe = e;
			}
		}
		if(minadj > ds[i]){ throw __LINE__; }
		if(pe.first >= 0){
			res1[i] = 'B';
			res1[pe.first] = 'W';
			res2[pe.second] = ds[i];
			for(const auto &e : G[i]){
				int v = e.first;
				pq.emplace(-ds[v], v);
			}
			for(const auto &e : G[pe.first]){
				int v = e.first;
				pq.emplace(-ds[v], v);
			}
		}
	}
	while(!pq.empty()){
		int u = pq.top().second;
		pq.pop();
		if(res1[u] != '?'){ continue; }
		int mindv = n;
		int eidx = -1;
		for(const pii &e : G[u]){
			int v = e.first;
			if(res1[v] != '?' && ds[mindv] > ds[v]){
				mindv = v;
				eidx = e.second;
			}
			pq.emplace(-ds[v], v);
		}
		if(eidx < 0){
			res1[u] = 'B';
		}
		else if(ds[mindv] > ds[u]){
			throw __LINE__;
		}
		else{
			res1[u] = res1[mindv] ^ 'B' ^ 'W';
			res2[eidx] = ds[u];
		}
	}

	if(count(res1.begin(), res1.end(), '?') > 0){ throw __LINE__; }
	puts(res1.c_str());
	for(int x : res2){ printf("%d\n", x); }
}
catch(int ln){
	fprintf(stderr, "catch %d\n", ln);
	puts("-1");
}