E. Optimize!
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Manao is solving a problem with the following statement:

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 answerf(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, ..., blen (1 ≤ bi ≤ 109). The third line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

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

Examples
Input
5 2 105 31 8 5 5 7
Output
2