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 sys
from bisect import bisect_left

def binary_search(a, x, lo=0, hi=None):  # can't use a to specify default for hi
    hi = hi if hi is not None else len(a)  # hi defaults to len(a)   
    pos = bisect_left(a, x, lo, hi)  # find insertion position
    return (pos if pos != hi and a[pos] == x else -1)  # don't walk off the end

def main():
	inp = input().split()
	number_of_programmers = int(inp[0])
	number_of_pairs = int(inp[1])
	number_of_programmers_can_help = [0] * number_of_programmers

	#Inicializar arreglo de programadores
	programmers_hability_unordered = [0] * number_of_programmers

	#Leer la habilidad de cada programador
	hability = input().split()
	for i in range(0,number_of_programmers):
		programmers_hability_unordered[i] = int(hability[i])

	#Ordenar el arreglo de programadores (nlogn)
	programmers_hability_ordered = programmers_hability_unordered.copy()
	programmers_hability_ordered.sort()

	#Guardar en qué posición del arreglo queda cada programador, y el número de programadores a los cuales puede ayudar (nlogn)
	for i in range(0,number_of_programmers):
		position = int((number_of_programmers-1)/2)
		#Búsqueda binaria
		position = binary_search(programmers_hability_ordered, programmers_hability_unordered[i])

		number_of_programmers_can_help[i] = position
		index = 1
		if position != 0:
			while (programmers_hability_ordered[position] == programmers_hability_ordered[position - index]):
				number_of_programmers_can_help[i] -= 1
				index+=1

	number_of_programmers_untouched = number_of_programmers_can_help.copy()
	#Leer las parejas ordenadas
	for i in range(0,number_of_pairs):
		quarrel = input().split()
		p1 = int(quarrel[0]) - 1
		p2 = int(quarrel[1]) - 1
		if number_of_programmers_untouched[p1] > number_of_programmers_untouched[p2]:
			#El primero pierde un programador al que ayudar
			number_of_programmers_can_help[p1] -= 1
		elif number_of_programmers_untouched[p1] < number_of_programmers_untouched[p2]:
			#El segundo pierde un programador al que ayudar
			number_of_programmers_can_help[p2] -= 1
		

	for i in range(0,number_of_programmers):
		sys.stdout.write(str(number_of_programmers_can_help[i]) + " ")

if __name__ == "__main__":
	main()