In BerSoft n programmers work, the programmer i is characterized by a skill r_i.

A programmer a can be a mentor of a programmer b if and only if the skill of the programmer a is strictly greater than the skill of the programmer b (r_a > r_b) and programmers a and b are not in a quarrel.

You are given the skills of each programmers and a list of k pairs of the programmers, which are in a quarrel (pairs are unordered). For each programmer i, find the number of programmers, for which the programmer i can be a mentor.

Input

The first line contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5, 0 ≤ k ≤ min(2 ⋅ 10^5, (n ⋅ (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, ..., r_n (1 ≤ r_i ≤ 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 ≤ x, y ≤ n, x ≠ 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.

Examples

Input

4 2
10 4 10 15
1 2
4 3


Output

0 0 1 2 


Input

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


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.
import java.lang.reflect.Array;
import java.util.*;
import java.util.stream.Collectors;

public class Mentors {

    public static int lowerBound(List<Integer> array, int length, int value) {
        int low = 0;
        int high = length;
        while (low < high) {
            final int mid = (low + high) / 2;
            if (value <= array.get(mid)) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }
        return low;
    }

    public static void main (String[] args) {
        Scanner reader = new Scanner(System.in);
        int n = reader.nextInt();
        int k = reader.nextInt();
        List<Programmer> programmers = new ArrayList<>();
        List<Integer> rates = new ArrayList<>();
        List<Minimalist> minimalists = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            int rate = reader.nextInt();
            programmers.add(new Programmer(rate, i));
            rates.add(rate);
        }
        for (int i = 0; i < k; i++) {
            int p1 = reader.nextInt();
            int p2 = reader.nextInt();
            programmers.get(p1 - 1).tryAdd(p2 - 1, programmers.get(p2 - 1).rate);
            programmers.get(p2 - 1).tryAdd(p1 - 1, programmers.get(p1 - 1).rate);
        }
        Collections.sort(programmers);
        Collections.sort(rates);
        for (int i = 0; i < n; i++) {
            Programmer programmer = programmers.get(i);
            int rate = programmer.rate;
            int lowerBound = lowerBound(rates, rates.size(), rate);
            int count = lowerBound;
            //System.out.println("lower bound for " + rate + " is " + lowerBound);
            count -= programmer.argue.size();
            minimalists.add(new Minimalist(programmer.index, count));
        }
        Collections.sort(minimalists);
        for (int i = 0; i < n; i++) {
            System.out.print(minimalists.get(i).count + " ");
        }
    }

}

class Minimalist implements Comparable {
    public Integer index;
    public int count;

    public Minimalist (int Index, int Count) {
        index = Index;
        count = Count;
    }

    @Override
    public int compareTo(Object o) {
        Minimalist other = (Minimalist) o;
        return index.compareTo(other.index);
    }
}

class Programmer implements Comparable {
    public Set<Integer> argue = new HashSet<>();
    public int index;
    public Integer rate;

    public Programmer (int Rate, int Index) {
        rate = Rate;
        index = Index;
    }

    public void tryAdd (int arg, int r) {
        if (r < rate) argue.add(arg);
    }

    @Override
    public int compareTo(Object o) {
        Programmer other = (Programmer)o;
        return rate.compareTo(other.rate);
    }
}
