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 <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <iomanip>
#include <queue>
#include <stack>
#include <cstdlib>
#include <map>
#include <iomanip>
#include <set>
#include <stdio.h>
#include <ctype.h>
#include <random>
#include <string.h>
#include <cmath>
#include <unordered_map>
#include <cstdio>
using namespace std;
#define all(vec) vec.begin(),vec.end()
typedef long long ll;

ll gcd(ll x, ll y) {
	if (y == 0)return x;
	return gcd(y, x%y);
}
ll lcm(ll x, ll y) {
	return x / gcd(x, y)*y;
}
ll kai(ll x, ll y, ll m) {
	ll res = 1;
	for (ll i = x - y + 1; i <= x; i++) {
		res *= i; res %= m;
	}
	return res;
}
ll mod_pow(ll x, ll y, ll m) {
	ll res = 1;
	while (y > 0) {
		if (y & 1) {
			res = res * x % m;
		}
		x = x * x % m;
		y >>= 1;
	}
	return res;
}

ll comb(ll x, ll y, ll m) {
	if (y > x)return 0;
	return kai(x, y, m) * mod_pow(kai(y, y, m), m - 2, m) % m;
}

int n, m, a[200010], b[200010], d[100010];
pair<int, int> p[100010];
int ans1[100010];
int ans2[200010];
vector<pair<int,int>> vec[100010];
bool bl1[200010], bl2[100010];

signed main() {
	cin >> n >> m;
	for (int i = 0; i < n; i++) {
		cin >> d[i + 1];
		p[i].first = d[i + 1];
		p[i].second = i + 1;
	}
	for (int i = 0; i < m; i++) {
		cin >> a[i] >> b[i];
		vec[a[i]].push_back(make_pair(b[i], i));
		vec[b[i]].push_back(make_pair(a[i], i));
	}
	sort(p, p + n);
	for (int i = 0; i < n; i++) {
		int k = p[i].second;
		if (bl2[k])continue;
		bool bo = false;
		for (int j = 0; j < (int)vec[k].size(); j++) {
			if (d[vec[k][j].first] <= d[k]) {
				bo = true;
				ans2[vec[k][j].second] = d[k];
				ans1[k] = 1 - ans1[vec[k][j].first];
				bl2[vec[k][j].first] = true;
				break;
			}
		}
		if (!bo) {
			cout << -1 << endl;
			return 0;
		}
	}
	for (int i = 1; i <= n; i++) {
		if (ans1[i] == 0)cout << 'W';
		else cout << 'B';
	}
	cout << endl;
	for (int i = 0; i < m; i++) {
		if (ans2[i] == 0)cout << 1000000000 << endl;
		else cout << ans2[i] << endl;
	}
}