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.util.*;

public class F {

    public static void main(String[] args) throws IOException {
        init(System.in);
        int n = nextInt(), k = nextInt();
        int[] r = new int[n];
        int[] unsorted = new int[n];
        for (int i = 0; i < r.length; i++) {
            r[i] = nextInt();
            unsorted[i] = r[i];
        }

        int[] sub = new int[n];
        for (int i = 0; i < k; i++) {
            int p1 = nextInt(), p2 = nextInt();
            if (r[p1 - 1] > r[p2 - 1]) sub[p1 - 1]++;
            else if (r[p1 - 1] < r[p2 - 1]) sub[p2 - 1]++;
        }

        ArrayList<Integer>  rr = new ArrayList<>();
        for (int aR : r) rr.add(aR);

        Collections.sort(rr);

        int[] ans = new int[n];
        Map<Integer, Integer> positions = new HashMap<>();
        for (int i = 0; i < rr.size(); i++) {
            if (!positions.containsKey(rr.get(i))) positions.put(rr.get(i), i);
        }
        for (int i = 0; i < n; i++) {
//            int pos = lowerBound(r, r.length, progToSkill.get(i));
            int pos = positions.get(unsorted[i]);
            ans[i] += (pos - sub[i]);
        }

//        System.out.println(Arrays.toString(ans).replace(", ", " ").replace("[", "").replace("]", ""));
        for (int a: ans) System.out.print(a + " ");

    }


    //Input Reader
    private static BufferedReader reader;
    private static StringTokenizer tokenizer;

    private static void init(InputStream inputStream) {
        reader = new BufferedReader(new InputStreamReader(inputStream));
        tokenizer = new StringTokenizer("");
    }

    private static String next() throws IOException {
        String read;
        while (!tokenizer.hasMoreTokens()) {
            read = reader.readLine();
            if (read == null || read.equals(""))
                return "-1";
            tokenizer = new StringTokenizer(read);
        }

        return tokenizer.nextToken();
    }

    private static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

//    private static long nextLong() throws IOException {
//        return Long.parseLong(next());
//    }
//
//    //    Get a whole line.
//    private static String line() throws IOException {
//        return reader.readLine();
//    }
//
//    private static double nextDouble() throws IOException {
//        return Double.parseDouble(next());
//    }
}

