Fair

Description:

Input:

There are $$$4$$$ integers $$$n$$$, $$$m$$$, $$$k$$$, $$$s$$$ in the first line of input ($$$1 \le n \le 10^{5}$$$, $$$0 \le m \le 10^{5}$$$, $$$1 \le s \le k \le min(n, 100)$$$) — the number of towns, the number of roads, the number of different types of goods, the number of different types of goods necessary to hold a fair.

In the next line there are $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_{i} \le k$$$), where $$$a_i$$$ is the type of goods produced in the $$$i$$$-th town. It is guaranteed that all integers between $$$1$$$ and $$$k$$$ occur at least once among integers $$$a_{i}$$$.

In the next $$$m$$$ lines roads are described. Each road is described by two integers $$$u$$$ $$$v$$$ ($$$1 \le u, v \le n$$$, $$$u \ne v$$$) — the towns connected by this road. It is guaranteed that there is no more than one road between every two towns. It is guaranteed that you can go from any town to any other town via roads.

Output:

Print $$$n$$$ numbers, the $$$i$$$-th of them is the minimum number of coins you need to spend on travel expenses to hold a fair in town $$$i$$$. Separate numbers with spaces.

Sample Input:

5 5 4 3
1 2 4 3 2
1 2
2 3
3 4
4 1
4 5

Sample Output:

2 2 2 2 3 

Sample Input:

7 6 3 2
1 2 3 3 2 2 1
1 2
2 3
3 4
2 5
5 6
6 7

Sample Output:

1 1 1 2 2 1 1 

Note:

Let's look at the first sample.

To hold a fair in town $$$1$$$ you can bring goods from towns $$$1$$$ ($$$0$$$ coins), $$$2$$$ ($$$1$$$ coin) and $$$4$$$ ($$$1$$$ coin). Total numbers of coins is $$$2$$$.

Town $$$2$$$: Goods from towns $$$2$$$ ($$$0$$$), $$$1$$$ ($$$1$$$), $$$3$$$ ($$$1$$$). Sum equals $$$2$$$.

Town $$$3$$$: Goods from towns $$$3$$$ ($$$0$$$), $$$2$$$ ($$$1$$$), $$$4$$$ ($$$1$$$). Sum equals $$$2$$$.

Town $$$4$$$: Goods from towns $$$4$$$ ($$$0$$$), $$$1$$$ ($$$1$$$), $$$5$$$ ($$$1$$$). Sum equals $$$2$$$.

Town $$$5$$$: Goods from towns $$$5$$$ ($$$0$$$), $$$4$$$ ($$$1$$$), $$$3$$$ ($$$2$$$). Sum equals $$$3$$$.