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.
'''4 2
10 4 10 15
1 2
4 3
'''

class Proger:
  def __init__(self, skill, proger_id):
    self.skill = skill
    self.proger_id = proger_id

  def __repr__(self):
    return '{id}: {skill}'.format(id=self.proger_id, skill=self.skill)

from collections import defaultdict

def main():
  _, k = map(int, input().strip().split(' '))
  progers = []
  argues = defaultdict(int)
  counter = 1
  
  for skill in input().strip().split(' '):
    sk = int(skill)
    progers.append(Proger(sk, counter))
    counter += 1


  skills_sorted = sorted(
    progers, 
    key=lambda proger: proger.skill
  )

  for _ in range(k):
    p1, p2 = map(int, input().strip().split(' '))
    if progers[p1 - 1].skill > progers[p2 - 1].skill:
      argues[p1] += 1
    
    if progers[p2 - 1].skill > progers[p1 - 1].skill:
      argues[p2] += 1

  # print('Argues', argues)

  padawan_counter = defaultdict(int)
  for idx in range(1, len(skills_sorted)):
    proger = skills_sorted[idx]
    prev_proger = skills_sorted[idx - 1]
    if prev_proger.skill < proger.skill:
      padawan_counter[proger.skill] = idx

  # print('Padawans', padawan_counter)

  res = []
  for proger in progers:
    res.append(padawan_counter[proger.skill] - argues[proger.proger_id])

  print(' '.join(str(count) for count in res))


if __name__ == '__main__':
  main()