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 Mentors {

	public static void main(String[] args) throws IOException{
		// TODO Auto-generated method stub
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out);
		StringTokenizer st = new StringTokenizer(br.readLine());
		int N = Integer.parseInt(st.nextToken()), K = Integer.parseInt(st.nextToken());
		ArrayList<state> arr = new ArrayList<state>();
		st = new StringTokenizer(br.readLine());
		for(int i = 0; i < N; ++i) {
			arr.add(new state(Integer.parseInt(st.nextToken()),0,i));
		}
		for(int i = 0; i < K; ++i) {
			st = new StringTokenizer(br.readLine());
			int a = Integer.parseInt(st.nextToken())-1, b = Integer.parseInt(st.nextToken())-1;
			state a1 = arr.get(a), b1 = arr.get(b);
			if(a1.sk > b1.sk) {
				++a1.q;
			}
			if(b1.sk > a1.sk) {
				++b1.q;
			}
		}
		Collections.sort(arr);
		int ans[] = new int[N];
		for(int i = 0; i < N; ++i) {
			state temp = arr.get(i);
			int a = 0, b = N-1;
			while(a!=b) {
				int mid = (a+b)/2;
				if(arr.get(mid).sk >= temp.sk) {
					b = mid;
				}else {
					a = mid+1;
				}
			}
			ans[temp.d] = a-temp.q;
		}
		for(int i = 0; i < N; ++i) pw.print(ans[i]+" ");
		//System.out.println(arr);
		pw.println();
		pw.close();
		br.close();
	}
	public static class state implements Comparable<state> {
		int sk, q, d;
		public state(int sk, int q, int d) {
			this.sk = sk; this.q = q; this.d = d;
		}
		public String toString() {
			return this.sk + " " + this.q + " " + this.d;
		}
		@Override
		public int compareTo(Mentors.state o) {
			// TODO Auto-generated method stub
			return sk-o.sk;
		}
	}

}
