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;

typedef long long ll;
const int maxn = 200005, maxm = 200005;

inline int gi()
{
    char c = getchar();
    while (c < '0' || c > '9') c = getchar();
    int sum = 0;
    while ('0' <= c && c <= '9') sum = sum * 10 + c - 48, c = getchar();
    return sum;
}

#define pb push_back

int n, m, d[maxn];

struct edge
{
    int to, next,vis;
} e[maxm * 2];
int h[maxn], tot = 1;
int w[maxm], col[maxn], fa[maxn], fe[maxn];
vector<int> vec[maxn];

inline void add(int u, int v)
{
    e[++tot] = (edge) {v, h[u]}; h[u] = tot;
    e[++tot] = (edge) {u, h[v]}; h[v] = tot;
}

void dfs(int u)
{
    for (int i=h[u];i;i=e[i].next) {
	if(!e[i].vis)continue;
	int v=e[i].to;
	if (col[v] == -1) col[v] = 1-col[u] , dfs(v);
    }
}

int main()
{
    n = gi(); m = gi();
    for (int i = 1; i <= n; ++i) d[i] = gi();
    for (int i = 1; i <= m; ++i) add(gi(), gi());
    fill(w + 1, w + m + 1, 1e9);

    d[0] = 2e9;
    for (int u = 1; u <= n; ++u) {
	if(!h[u])return puts("-1"), 0;;
	int p=h[u];
	for(int i=e[p].next;i;i=e[i].next){
	    if(d[e[i].to]<d[e[p].to])p=i;
	    else if(d[e[i].to]==d[e[p].to]&&e[i].to<e[p].to)p=i;
	}
	if (d[e[p].to] > d[u]) return puts("-1"), 0;
	w[p>>1]=d[u];fa[u] = e[p].to;e[p^1].vis=1;
    }
	
    fill(col + 1, col + n + 1, -1);
    for (int i = 1; i <= n; ++i) if (fa[fa[i]] == i && col[i] == -1) col[i] = 0, dfs(i); 
    for (int i = 1; i <= n; ++i) putchar(col[i] == 0 ? 'B' : 'W');
    puts("");
    for (int i = 1; i <= m; ++i) printf("%d\n", w[i]);
	
    return 0;
}