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Robocity has $n$ crossroads connected by bidirectional roads. There are $m$ roads in total, and all crossroads are reachable from each other. There is a level assigned to each crossroad specified by a number from $1$ to $k$, inclusive. Any pair of crossroads directly connected by a road has distinct levels.
The city leaders are planning a reform. Namely, they want to assign new levels to crossroads, so that each level still has a value from $1$ to $k$, connected crossroads would have different levels, and an additional condition has to be met: for each pair of crossroads $u$ and $v$ there must exist a path between them, such that any two adjacent crossroads along it have levels that differ by $1$ modulo $k$.
Formally, for each pair of crossroads $(u, v)$ there should exist a sequence of crossroads $p_1, \ldots, p_l$, such that:
Robocity government is convinced that such level assignment exists and asks you to find it.
The first line contains three integers $n$, $m$, $k$ ($1 \le n, m, k \le 500000$), number of crossroads, roads, and levels.
The second line contains $n$ integers $c_1, c_2, \ldots, c_n$ ($1 \le c_i \le k$), $c_i$ is the level of the crossroad $i$.
Then $m$ lines follow, each of them contains two integers $u$, $v$ ($1 \le u, v \le n, u \neq v$), a pairs of crossroads connected by a road.
It is guaranteed that there are no two roads connecting the same pair of crossroads, and that there exists a path between each pair of crossroads.
Output $n$ integers $d_1, d_2, \ldots, d_n$ ($1 \le d_i \le k$), the levels of the crossroads in the new assignment.
4 4 4 1 2 3 1 1 2 1 3 2 3 3 4
4 3 2 1