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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashSet;
import java.util.StringTokenizer;

public class Mentors {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        Pair[] arr = new Pair[n];
        int[] lookup = new int[n];
        st = new StringTokenizer(br.readLine());
        for (int i = 0; i < n; i++) {
            arr[i] = new Pair(Integer.parseInt(st.nextToken()), i);
            lookup[i] = arr[i].a;
        }
        Arrays.sort(arr);
        HashSet<Integer>[] quarrels = new HashSet[n];
        for (int i = 0; i < n; i++) {
            quarrels[i] = new HashSet<>();
        }
        for (int i = 0; i < k; i++) {
            st = new StringTokenizer(br.readLine());
            int a = Integer.parseInt(st.nextToken()) - 1;
            int b = Integer.parseInt(st.nextToken()) - 1;
            quarrels[a].add(b);
            quarrels[b].add(a);
        }
        HashSet<Integer> done = new HashSet<>();
        int[] answers = new int[n];
        int prev = 0;
        int prevCount = 0;
        //HashSet<Integer> same = new HashSet<>();
        for (int i = 0; i < n; i++) {
            if (arr[i].a == prev) {
                prevCount++;
            } else {
                prevCount = 0;
            }
            int count = 0;
            for (int j : quarrels[arr[i].b]) {
                if (done.contains(j) && lookup[j] != arr[i].a) {
                    count++;
                }
            }
            answers[arr[i].b] = Math.max(0, done.size() - prevCount - count);
            done.add(arr[i].b);
            prev = arr[i].a;
        }
        for (int i : answers) {
            System.out.print(i + " ");
        }
    }

    static class Pair implements Comparable<Pair>{
        int a, b;

        public Pair(int a, int b) {
            this.a = a;
            this.b = b;
        }

        public int compareTo(Pair o) {
            return Integer.compare(a, o.a);
        }
    }
}
