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:
/* cerberus97 - Hanit Banga */

#include <iostream>
#include <iomanip>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <vector>
#include <algorithm>
#include <numeric>

using namespace std;

#define pb push_back
#define fast_cin() ios_base::sync_with_stdio(false); cin.tie(NULL)

typedef long long ll;
typedef long double ld;
typedef pair <int, int> pii;
typedef pair <ll, ll> pll;

const int N = 1e5 + 10, M = 2e5 + 10;

int d[N], u[M], v[M];
vector<int> g[N];

void dfs(int u, int wt, string& colors, char c);

int main() {
	fast_cin();
	int n, m;
	cin >> n >> m;
	for (int i = 1; i <= n; ++i) {
		cin >> d[i];
	}
	for (int i = 1; i <= m; ++i) {
		cin >> u[i] >> v[i];
		g[u[i]].pb(v[i]);
		g[v[i]].pb(u[i]);
	}
	vector<int> ids(n);
	iota(ids.begin(), ids.end(), 1);
	sort(ids.begin(), ids.end(), [&] (int i, int j) {
		return tie(d[i], i) < tie(d[j], j);
	});
	for (int i = 1; i <= n; ++i) {
		sort(g[i].begin(), g[i].end(), [&] (int x, int y) {
			return tie(d[x], x) < tie(d[y], y);
		});
	}
	string colors(n, 'A');
	for (auto& i : ids) {
		if (d[g[i][0]] > d[i]) {
			cout << -1 << endl;
			return 0;
		} else if (d[g[i][0]] < d[i]) {
			continue;
		} else if (colors[i - 1] == 'A') {
			dfs(i, d[i], colors, 'B');
		}
	}
	for (int i = 0; i < n; ++i) {
		if (colors[i] == 'A') {
			colors[i] = 'B';
		}
	}
	cout << colors << '\n';
	for (int i = 1; i <= m; ++i) {
		if (colors[u[i] - 1] == colors[v[i] - 1]) {
			cout << max(1, abs(d[u[i]] - d[v[i]])) << '\n';
		} else {
			cout << max(d[u[i]], d[v[i]]) << '\n';
		}
	}
}

void dfs(int u, int wt, string& colors, char c) {
	colors[u - 1] = 'B' ^ 'W' ^ c;
	for (auto& v : g[u]) {
		if (d[v] > wt) {
			break;
		} else if (colors[v - 1] == 'A') {
			dfs(v, wt, colors, colors[u - 1]);
		}
	}
}