Manao is solving a problem with the following statement:

$\text{[math]}$

He came up with a solution that produces the correct answers but is too slow. You are given the pseudocode of his solution, where the function getAnswer calculates the answer to the problem:


getAnswer(a[1..n], b[1..len], h)
  answer = 0
  for i = 1 to n-len+1
    answer = answer + f(a[i..i+len-1], b, h, 1)
  return answer

f(s[1..len], b[1..len], h, index)
  if index = len+1 then
    return 1
  for i = 1 to len
    if s[index] + b[i] >= h
      mem = b[i]
      b[i] = 0
      res = f(s, b, h, index + 1)
      b[i] = mem
      if res > 0
        return 1
  return 0

Your task is to help Manao optimize his algorithm.

Input

The first line contains space-separated integers n, len and h (1 ≤ len ≤ n ≤ 150000; 1 ≤ h ≤ 10⁹). The second line contains len space-separated integers b₁, b₂, ..., b_len (1 ≤ b_i ≤ 10⁹). The third line contains n space-separated integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁹).

Output

Print a single number — the answer to Manao's problem.

Optimize!

Examples