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.*;
import java.lang.reflect.Array;
import java.util.*;
public class dd {
    public static void main(String args[]) throws IOException {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader sc = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);

        int n = sc.nextInt(), k = sc.nextInt();
        pair[] a = new pair[n];
        ArrayList<Integer>[] g = new ArrayList[n];
        for (int i = 0; i < n; i++)
            g[i] = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            a[i] = new pair(i, sc.nextInt());
        }

        for (int i = 0; i < k; i++) {
            int x = sc.nextInt() - 1, y = sc.nextInt() - 1;
            if (a[x].skill > a[y].skill)
                g[x].add(y);
            else if (a[y].skill > a[x].skill)
                g[y].add(x);
        }
        Arrays.sort(a, (c, b) -> Integer.compare(c.skill, b.skill));
        int[] ans = new int[n];
        for (int i = 0; i < n; i++) {
            int r = n - 1, l = 0, t = 0;
            while (r >= l) {
                int m = (r + l) / 2;
                if (a[m].skill < a[i].skill)
                    l = m + 1;
                else {
                    r = m - 1;
                    t = m;
                }
            }
            ans[a[i].pos] = Math.max(0, t - g[a[i].pos].size());
        }
        for (int i = 0; i < n; i++)
            System.out.print(ans[i] + " ");
        out.close();
    }


    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}
class pair{
    int pos,skill;
    pair(int pos,int skill){
        this.pos=pos;
        this.skill=skill;
    }
}