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 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]  \ge  h
 mem = b[i]
 b[i] = 0
 res = f(s, b, h, index + 1)
 b[i] = mem
 if res  \gt  0
 return 1
 return 0

Your task is to help Manao optimize his algorithm.

The first line contains space-separated integers n, len and h (1 \le len \le n \le 150000;1 \le h \le 109). The second line contains len space-separated integers b1,b2,...,blen (1 \le bi \le 109). The third line contains n space-separated integers a1,a2,...,an (1 \le ai \le 109).

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