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;
 
//#pragma GCC optimize("O3")
//#pragma GCC target("sse4")
 
#define FOR(i, a, b) for(int i = (a); i < (b); ++i)
#define RFOR(i, b, a) for(int i = (b) - 1; i >= (a); --i)
#define ITER(it, a) for(__typeof(a.begin()) it = a.begin(); it != a.end(); it++)
#define FILL(a, value) memset(a, value, sizeof(a))
 
#define SZ(a) (int)((a).size())
#define ALL(a) a.begin(), a.end()
#define PB push_back
#define MP make_pair
 
typedef long long LL;
typedef pair<int, int> PII;
 
const double PI = acos(-1.0);
const int INF = 1000 * 1000 * 1000;
const LL LINF = (LL)INF * INF;

const int MAX = 1 << 18;

int d[MAX];
vector<PII> g[MAX];
char s[MAX];
int ver[MAX];
int c[MAX];

bool cmp(int u, int v)
{
	return d[u] != d[v] ? d[u] < d[v] : u < v;
}

bool cmp2(PII u, PII v)
{
	return cmp(u.first, v.first);
}

int main()
{
	ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
	int n, m;
	cin >> n >> m;
	FOR(i, 0, n)
	{
		s[i] = 'Q';
		cin >> d[i];
		ver[i] = i;
	}
	s[n] = '\0';
	FOR(i, 0, m)
	{
		int u, v;
		cin >> u >> v;
		u--;
		v--;
		g[u].PB(MP(v, i));
		g[v].PB(MP(u, i));
		c[i] = INF;
	}
	sort(ver, ver + n, cmp);
	FOR(i, 0, n)
	{
		PII to = MP(-1, -1);
		for(PII x: g[ver[i]])
			if(d[x.first] <= d[ver[i]] && (to == MP(-1, -1) || s[x.first] != 'Q'))
				to = x;
		if(to.first == -1)
		{
			cout << "-1\n";
			return 0;
		}
		c[to.second] = d[ver[i]];
		if(s[ver[i]] == 'Q')
		{
			if(s[to.first] == 'Q')
				s[to.first] = 'B';
			s[ver[i]] = s[to.first] == 'W' ? 'B' : 'W';
		}
		if(s[to.first] == 'Q')
			s[to.first] = s[ver[i]] == 'W' ? 'B' : 'W';
	}
	cout << s << "\n";
	FOR(i, 0, m)
		cout << c[i] << "\n";
	return 0;
}