Mentors

Description:

Input:

The first line contains two integers $$$n$$$ and $$$k$$$ $$$(2 \le n \le 2 \cdot 10^5$$$, $$$0 \le k \le \min(2 \cdot 10^5, \frac{n \cdot (n - 1)}{2}))$$$ — total number of programmers and number of pairs of programmers which are in a quarrel.

The second line contains a sequence of integers $$$r_1, r_2, \dots, r_n$$$ $$$(1 \le r_i \le 10^{9})$$$, where $$$r_i$$$ equals to the skill of the $$$i$$$-th programmer.

Each of the following $$$k$$$ lines contains two distinct integers $$$x$$$, $$$y$$$ $$$(1 \le x, y \le n$$$, $$$x \ne y)$$$ — pair of programmers in a quarrel. The pairs are unordered, it means that if $$$x$$$ is in a quarrel with $$$y$$$ then $$$y$$$ is in a quarrel with $$$x$$$. Guaranteed, that for each pair $$$(x, y)$$$ there are no other pairs $$$(x, y)$$$ and $$$(y, x)$$$ in the input.

Output:

Print $$$n$$$ integers, the $$$i$$$-th number should be equal to the number of programmers, for which the $$$i$$$-th programmer can be a mentor. Programmers are numbered in the same order that their skills are given in the input.

Sample Input:

4 2
10 4 10 15
1 2
4 3

Sample Output:

0 0 1 2 

Sample Input:

10 4
5 4 1 5 4 3 7 1 2 5
4 6
2 1
10 8
3 5

Sample Output:

5 4 0 5 3 3 9 0 2 5 

Note:

In the first example, the first programmer can not be mentor of any other (because only the second programmer has a skill, lower than first programmer skill, but they are in a quarrel). The second programmer can not be mentor of any other programmer, because his skill is minimal among others. The third programmer can be a mentor of the second programmer. The fourth programmer can be a mentor of the first and of the second programmers. He can not be a mentor of the third programmer, because they are in a quarrel.